1152 lines
44 KiB
Python
1152 lines
44 KiB
Python
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 numpy as np
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import pandas as pd
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import h5py
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from scipy import ndimage, spatial
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from . import VTK
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from . import util
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from . import grid_filters
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from . import Rotation
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class Grid:
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"""
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Geometry definition for grid solvers.
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Create and manipulate geometry definitions for storage as VTK
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image data files ('.vti' extension). A grid contains the
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material ID (referring to the entry in 'material.yaml') and
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the physical size.
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"""
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def __init__(self,material,size,origin=[0.0,0.0,0.0],comments=[]):
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"""
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New geometry definition for grid solvers.
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Parameters
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----------
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material : numpy.ndarray of shape (:,:,:)
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Material indices. The shape of the material array defines
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the number of cells.
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size : list or numpy.ndarray of shape (3)
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Physical size of grid in meter.
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origin : list or numpy.ndarray of shape (3), optional
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Coordinates of grid origin in meter.
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comments : list of str, optional
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Comments, e.g. history of operations.
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"""
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self.material = material
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self.size = size
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self.origin = origin
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self.comments = comments
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def __repr__(self):
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"""Basic information on grid definition."""
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mat_min = np.nanmin(self.material)
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mat_max = np.nanmax(self.material)
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mat_N = self.N_materials
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return util.srepr([
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f'cells : {util.srepr(self.cells, " x ")}',
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f'size : {util.srepr(self.size, " x ")} / m³',
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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
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f' (min: {mat_min}, max: {mat_max})')
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])
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def __copy__(self):
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"""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):
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"""
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Test equality of other.
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Parameters
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----------
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other : damask.Grid
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Grid to compare self against.
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"""
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return (np.allclose(other.size,self.size)
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and np.allclose(other.origin,self.origin)
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and np.all(other.cells == self.cells)
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and np.all(other.material == self.material))
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@property
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def material(self):
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"""Material indices."""
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return self._material
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@material.setter
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def material(self,material):
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if len(material.shape) != 3:
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raise ValueError(f'invalid material shape {material.shape}')
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elif material.dtype not in np.sctypes['float'] + np.sctypes['int']:
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raise TypeError(f'invalid material data type {material.dtype}')
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else:
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self._material = np.copy(material)
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if self.material.dtype in np.sctypes['float'] and \
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np.all(self.material == self.material.astype(int).astype(float)):
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self._material = self.material.astype(int)
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@property
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def size(self):
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"""Physical size of grid in meter."""
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return self._size
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@size.setter
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def size(self,size):
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if len(size) != 3 or any(np.array(size) < 0):
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raise ValueError(f'invalid size {size}')
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else:
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self._size = np.array(size)
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@property
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def origin(self):
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"""Coordinates of grid origin in meter."""
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return self._origin
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@origin.setter
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def origin(self,origin):
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if len(origin) != 3:
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raise ValueError(f'invalid origin {origin}')
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else:
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self._origin = np.array(origin)
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@property
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def comments(self):
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"""Comments, e.g. history of operations."""
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return self._comments
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@comments.setter
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def comments(self,comments):
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self._comments = [str(c) for c in comments] if isinstance(comments,list) else [str(comments)]
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@property
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def cells(self):
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"""Number of cells in x,y,z direction."""
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return np.asarray(self.material.shape)
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@property
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def N_materials(self):
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"""Number of (unique) material indices within grid."""
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return np.unique(self.material).size
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@staticmethod
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def load(fname):
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"""
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Load from VTK image data file.
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Parameters
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----------
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fname : str or or pathlib.Path
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Grid file to read. Valid extension is .vti, which will be appended
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if not given.
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Returns
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-------
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loaded : damask.Grid
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Grid-based geometry from file.
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"""
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v = VTK.load(fname if str(fname).endswith(('.vti','.vtr')) else str(fname)+'.vti') # compatibility hack
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comments = v.get_comments()
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cells = np.array(v.vtk_data.GetDimensions())-1
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bbox = np.array(v.vtk_data.GetBounds()).reshape(3,2).T
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return Grid(material = v.get('material').reshape(cells,order='F'),
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size = bbox[1] - bbox[0],
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origin = bbox[0],
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comments=comments)
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@staticmethod
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def load_ASCII(fname):
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"""
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Load from geom file.
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Storing geometry files in ASCII format is deprecated.
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This function will be removed in a future version of DAMASK.
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Parameters
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----------
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fname : str, pathlib.Path, or file handle
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Geometry file to read.
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Returns
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-------
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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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try:
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f = open(fname)
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except TypeError:
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f = fname
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f.seek(0)
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try:
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header_length,keyword = f.readline().split()[:2]
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header_length = int(header_length)
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except ValueError:
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header_length,keyword = (-1, 'invalid')
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if not keyword.startswith('head') or header_length < 3:
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raise TypeError('header length information missing or invalid')
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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()
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key = items[0] if items else ''
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if key == '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':
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size = np.array([float(dict(zip(items[1::2],items[2::2]))[i]) for i in ['x','y','z']])
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elif key == 'origin':
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origin = np.array([float(dict(zip(items[1::2],items[2::2]))[i]) for i in ['x','y','z']])
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else:
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comments.append(line.strip())
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material = np.empty(cells.prod()) # initialize as flat array
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i = 0
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for line in content[header_length:]:
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items = line.split('#')[0].split()
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if len(items) == 3:
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if items[1].lower() == 'of':
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items = np.ones(int(items[0]))*float(items[2])
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elif items[1].lower() == 'to':
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items = 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: items = list(map(float,items))
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else: items = list(map(float,items))
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material[i:i+len(items)] = items
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i += len(items)
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if i != cells.prod():
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raise TypeError(f'invalid file: expected {cells.prod()} entries, found {i}')
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if not np.any(np.mod(material,1) != 0.0): # no float present
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material = material.astype('int') - (1 if material.min() > 0 else 0)
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return Grid(material.reshape(cells,order='F'),size,origin,comments)
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@staticmethod
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def load_Neper(fname):
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"""
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Load from Neper VTK file.
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Parameters
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----------
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fname : str, pathlib.Path, or file handle
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Geometry file to read.
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Returns
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-------
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loaded : damask.Grid
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Grid-based geometry from file.
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"""
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v = VTK.load(fname,'vtkImageData')
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cells = np.array(v.vtk_data.GetDimensions())-1
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bbox = np.array(v.vtk_data.GetBounds()).reshape(3,2).T
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return Grid(v.get('MaterialId').reshape(cells,order='F').astype('int32',casting='unsafe') - 1,
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bbox[1] - bbox[0], bbox[0],
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util.execution_stamp('Grid','load_Neper'))
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@staticmethod
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def load_DREAM3D(fname,
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feature_IDs=None,cell_data=None,
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phases='Phases',Euler_angles='EulerAngles',
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base_group=None):
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"""
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Load DREAM.3D (HDF5) file.
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Data in DREAM.3D files can be stored per cell ('CellData') and/or
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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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----------
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fname : str
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Filename of the DREAM.3D (HDF5) file.
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feature_IDs : str
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Name of the dataset containing the mapping between cells and
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grain-wise data. Defaults to 'None', in which case cell-wise
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data is used.
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cell_data : str
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Name of the group (folder) containing cell-wise data. Defaults to
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None in wich case it is automatically detected.
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phases : str
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Name of the dataset containing the phase ID. It is not used for
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grain-wise data, i.e. when feature_IDs is not None.
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Defaults to 'Phases'.
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Euler_angles : str
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Name of the dataset containing the crystallographic orientation as
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Euler angles in radians It is not used for grain-wise data, i.e.
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when feature_IDs is not None. Defaults to 'EulerAngles'.
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base_group : str
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Path to the group (folder) that contains geometry (_SIMPL_GEOMETRY),
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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.
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Returns
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-------
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loaded : damask.Grid
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Grid-based geometry from file.
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"""
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b = util.DREAM3D_base_group(fname) if base_group is None else base_group
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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'])][()]
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size = f['/'.join([b,'_SIMPL_GEOMETRY','SPACING'])] * cells
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origin = f['/'.join([b,'_SIMPL_GEOMETRY','ORIGIN'])][()]
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if feature_IDs is None:
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phase = f['/'.join([b,c,phases])][()].reshape(-1,1)
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O = Rotation.from_Euler_angles(f['/'.join([b,c,Euler_angles])]).as_quaternion().reshape(-1,4) # noqa
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unique,unique_inverse = np.unique(np.hstack([O,phase]),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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else:
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ma = f['/'.join([b,c,feature_IDs])][()].flatten()
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return Grid(ma.reshape(cells,order='F'),size,origin,util.execution_stamp('Grid','load_DREAM3D'))
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@staticmethod
|
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def from_table(table,coordinates,labels):
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"""
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||
Create grid from ASCII table.
|
||
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||
Parameters
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||
----------
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table : damask.Table
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Table that contains material information.
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coordinates : str
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Label of the vector column containing the spatial coordinates.
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||
Need to be ordered (1./x fast, 3./z slow).
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labels : str or list of str
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Label(s) of the columns containing the material definition.
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Each unique combination of values results in one material ID.
|
||
|
||
Returns
|
||
-------
|
||
new : damask.Grid
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Grid-based geometry from values in table.
|
||
|
||
"""
|
||
cells,size,origin = grid_filters.cellsSizeOrigin_coordinates0_point(table.get(coordinates))
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||
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labels_ = [labels] if isinstance(labels,str) else labels
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unique,unique_inverse = np.unique(np.hstack([table.get(l) for l in labels_]),return_inverse=True,axis=0)
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||
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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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||
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return Grid(ma.reshape(cells,order='F'),size,origin,util.execution_stamp('Grid','from_table'))
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||
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||
|
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@staticmethod
|
||
def _find_closest_seed(seeds, weights, point):
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||
return np.argmin(np.sum((np.broadcast_to(point,(len(seeds),3))-seeds)**2,axis=1) - weights)
|
||
|
||
@staticmethod
|
||
def from_Laguerre_tessellation(cells,size,seeds,weights,material=None,periodic=True):
|
||
"""
|
||
Create grid from Laguerre tessellation.
|
||
|
||
Parameters
|
||
----------
|
||
cells : int numpy.ndarray of shape (3)
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||
Number of cells in x,y,z direction.
|
||
size : list or numpy.ndarray of shape (3)
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||
Physical size of the grid in meter.
|
||
seeds : numpy.ndarray of shape (:,3)
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||
Position of the seed points in meter. All points need to lay within the box.
|
||
weights : numpy.ndarray of shape (seeds.shape[0])
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||
Weights of the seeds. Setting all weights to 1.0 gives a standard Voronoi tessellation.
|
||
material : numpy.ndarray of shape (seeds.shape[0]), optional
|
||
Material ID of the seeds.
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||
Defaults to None, in which case materials are consecutively numbered.
|
||
periodic : Boolean, optional
|
||
Assume grid to be periodic. Defaults to True.
|
||
|
||
Returns
|
||
-------
|
||
new : damask.Grid
|
||
Grid-based geometry from tessellation.
|
||
|
||
"""
|
||
if periodic:
|
||
weights_p = np.tile(weights,27) # Laguerre weights (1,2,3,1,2,3,...,1,2,3)
|
||
seeds_p = np.vstack((seeds -np.array([size[0],0.,0.]),seeds, seeds +np.array([size[0],0.,0.])))
|
||
seeds_p = np.vstack((seeds_p-np.array([0.,size[1],0.]),seeds_p,seeds_p+np.array([0.,size[1],0.])))
|
||
seeds_p = np.vstack((seeds_p-np.array([0.,0.,size[2]]),seeds_p,seeds_p+np.array([0.,0.,size[2]])))
|
||
else:
|
||
weights_p = weights
|
||
seeds_p = seeds
|
||
|
||
coords = grid_filters.coordinates0_point(cells,size).reshape(-1,3)
|
||
|
||
pool = mp.Pool(int(os.environ.get('OMP_NUM_THREADS',4)))
|
||
result = pool.map_async(partial(Grid._find_closest_seed,seeds_p,weights_p), coords)
|
||
pool.close()
|
||
pool.join()
|
||
material_ = np.array(result.get()).reshape(cells)
|
||
|
||
if periodic: material_ %= len(weights)
|
||
|
||
return Grid(material = material_ if material is None else material[material_],
|
||
size = size,
|
||
comments = util.execution_stamp('Grid','from_Laguerre_tessellation'),
|
||
)
|
||
|
||
|
||
@staticmethod
|
||
def from_Voronoi_tessellation(cells,size,seeds,material=None,periodic=True):
|
||
"""
|
||
Create grid from Voronoi tessellation.
|
||
|
||
Parameters
|
||
----------
|
||
cells : int numpy.ndarray of shape (3)
|
||
Number of cells in x,y,z direction.
|
||
size : list or numpy.ndarray of shape (3)
|
||
Physical size of the grid in meter.
|
||
seeds : numpy.ndarray of shape (:,3)
|
||
Position of the seed points in meter. All points need to lay within the box.
|
||
material : numpy.ndarray of shape (seeds.shape[0]), optional
|
||
Material ID of the seeds.
|
||
Defaults to None, in which case materials are consecutively numbered.
|
||
periodic : Boolean, optional
|
||
Assume grid to be periodic. Defaults to True.
|
||
|
||
Returns
|
||
-------
|
||
new : damask.Grid
|
||
Grid-based geometry from tessellation.
|
||
|
||
"""
|
||
coords = grid_filters.coordinates0_point(cells,size).reshape(-1,3)
|
||
tree = spatial.cKDTree(seeds,boxsize=size) if periodic else \
|
||
spatial.cKDTree(seeds)
|
||
try:
|
||
material_ = tree.query(coords, workers = int(os.environ.get('OMP_NUM_THREADS',4)))[1]
|
||
except TypeError:
|
||
material_ = tree.query(coords, n_jobs = int(os.environ.get('OMP_NUM_THREADS',4)))[1] # scipy <1.6
|
||
|
||
return Grid(material = (material_ if material is None else material[material_]).reshape(cells),
|
||
size = size,
|
||
comments = util.execution_stamp('Grid','from_Voronoi_tessellation'),
|
||
)
|
||
|
||
|
||
_minimal_surface = \
|
||
{'Schwarz P': lambda x,y,z: np.cos(x) + np.cos(y) + np.cos(z),
|
||
'Double Primitive': lambda x,y,z: ( 0.5 * (np.cos(x)*np.cos(y) + np.cos(y)*np.cos(z) + np.cos(z)*np.cos(x))
|
||
+ 0.2 * (np.cos(2*x) + np.cos(2*y) + np.cos(2*z)) ),
|
||
'Schwarz D': lambda x,y,z: ( np.sin(x)*np.sin(y)*np.sin(z)
|
||
+ np.sin(x)*np.cos(y)*np.cos(z)
|
||
+ np.cos(x)*np.cos(y)*np.sin(z)
|
||
+ np.cos(x)*np.sin(y)*np.cos(z) ),
|
||
'Complementary D': lambda x,y,z: ( np.cos(3*x+y)*np.cos(z) - np.sin(3*x-y)*np.sin(z) + np.cos(x+3*y)*np.cos(z)
|
||
+ np.sin(x-3*y)*np.sin(z) + np.cos(x-y)*np.cos(3*z) - np.sin(x+y)*np.sin(3*z) ),
|
||
'Double Diamond': lambda x,y,z: 0.5 * (np.sin(x)*np.sin(y)
|
||
+ np.sin(y)*np.sin(z)
|
||
+ np.sin(z)*np.sin(x)
|
||
+ np.cos(x) * np.cos(y) * np.cos(z) ),
|
||
'Dprime': lambda x,y,z: 0.5 * ( np.cos(x)*np.cos(y)*np.cos(z)
|
||
+ np.cos(x)*np.sin(y)*np.sin(z)
|
||
+ np.sin(x)*np.cos(y)*np.sin(z)
|
||
+ np.sin(x)*np.sin(y)*np.cos(z)
|
||
- np.sin(2*x)*np.sin(2*y)
|
||
- np.sin(2*y)*np.sin(2*z)
|
||
- np.sin(2*z)*np.sin(2*x) ) - 0.2,
|
||
'Gyroid': lambda x,y,z: np.cos(x)*np.sin(y) + np.cos(y)*np.sin(z) + np.cos(z)*np.sin(x),
|
||
'Gprime': lambda x,y,z : ( np.sin(2*x)*np.cos(y)*np.sin(z)
|
||
+ np.sin(2*y)*np.cos(z)*np.sin(x)
|
||
+ np.sin(2*z)*np.cos(x)*np.sin(y) ) + 0.32,
|
||
'Karcher K': lambda x,y,z: ( 0.3 * ( np.cos(x) + np.cos(y) + np.cos(z)
|
||
+ np.cos(x)*np.cos(y) + np.cos(y)*np.cos(z) + np.cos(z)*np.cos(x) )
|
||
- 0.4 * ( np.cos(2*x) + np.cos(2*y) + np.cos(2*z) ) ) + 0.2,
|
||
'Lidinoid': lambda x,y,z: 0.5 * ( np.sin(2*x)*np.cos(y)*np.sin(z)
|
||
+ np.sin(2*y)*np.cos(z)*np.sin(x)
|
||
+ np.sin(2*z)*np.cos(x)*np.sin(y)
|
||
- np.cos(2*x)*np.cos(2*y)
|
||
- np.cos(2*y)*np.cos(2*z)
|
||
- np.cos(2*z)*np.cos(2*x) ) + 0.15,
|
||
'Neovius': lambda x,y,z: ( 3 * (np.cos(x)+np.cos(y)+np.cos(z))
|
||
+ 4 * np.cos(x)*np.cos(y)*np.cos(z) ),
|
||
'Fisher-Koch S': lambda x,y,z: ( np.cos(2*x)*np.sin( y)*np.cos( z)
|
||
+ np.cos( x)*np.cos(2*y)*np.sin( z)
|
||
+ np.sin( x)*np.cos( y)*np.cos(2*z) ),
|
||
}
|
||
|
||
|
||
@staticmethod
|
||
def from_minimal_surface(cells,size,surface,threshold=0.0,periods=1,materials=(0,1)):
|
||
"""
|
||
Create grid from definition of triply periodic minimal surface.
|
||
|
||
Parameters
|
||
----------
|
||
cells : int numpy.ndarray of shape (3)
|
||
Number of cells in x,y,z direction.
|
||
size : list or numpy.ndarray of shape (3)
|
||
Physical size of the grid in meter.
|
||
surface : str
|
||
Type of the minimal surface. See notes for details.
|
||
threshold : float, optional.
|
||
Threshold of the minimal surface. Defaults to 0.0.
|
||
periods : integer, optional.
|
||
Number of periods per unit cell. Defaults to 1.
|
||
materials : (int, int), optional
|
||
Material IDs. Defaults to (0,1).
|
||
|
||
Returns
|
||
-------
|
||
new : damask.Grid
|
||
Grid-based geometry from definition of minimal surface.
|
||
|
||
Notes
|
||
-----
|
||
The following triply-periodic minimal surfaces are implemented:
|
||
- Schwarz P
|
||
- Double Primitive
|
||
- Schwarz D
|
||
- Complementary D
|
||
- Double Diamond
|
||
- Dprime
|
||
- Gyroid
|
||
- Gprime
|
||
- Karcher K
|
||
- Lidinoid
|
||
- Neovius
|
||
- Fisher-Koch S
|
||
|
||
References
|
||
----------
|
||
S.B.G. Blanquer et al., Biofabrication 9(2):025001, 2017
|
||
https://doi.org/10.1088/1758-5090/aa6553
|
||
|
||
M. Wohlgemuth et al., Macromolecules 34(17):6083-6089, 2001
|
||
https://doi.org/10.1021/ma0019499
|
||
|
||
M.-T. Hsieh and L. Valdevit, Software Impacts 6:100026, 2020
|
||
https://doi.org/10.1016/j.simpa.2020.100026
|
||
|
||
Examples
|
||
--------
|
||
Minimal surface of 'Gyroid' type.
|
||
|
||
>>> import numpy as np
|
||
>>> import damask
|
||
>>> damask.Grid.from_minimal_surface(np.array([64]*3,int),np.ones(3),
|
||
... 'Gyroid')
|
||
cells a b c: 64 x 64 x 64
|
||
size x y z: 1.0 x 1.0 x 1.0
|
||
origin x y z: 0.0 0.0 0.0
|
||
# materials: 2
|
||
|
||
Minimal surface of 'Neovius' type. non-default material IDs.
|
||
|
||
>>> import numpy as np
|
||
>>> import damask
|
||
>>> damask.Grid.from_minimal_surface(np.array([80]*3,int),np.ones(3),
|
||
... 'Neovius',materials=(1,5))
|
||
cells a b c: 80 x 80 x 80
|
||
size x y z: 1.0 x 1.0 x 1.0
|
||
origin x y z: 0.0 0.0 0.0
|
||
# materials: 2 (min: 1, max: 5)
|
||
|
||
"""
|
||
x,y,z = np.meshgrid(periods*2.0*np.pi*(np.arange(cells[0])+0.5)/cells[0],
|
||
periods*2.0*np.pi*(np.arange(cells[1])+0.5)/cells[1],
|
||
periods*2.0*np.pi*(np.arange(cells[2])+0.5)/cells[2],
|
||
indexing='ij',sparse=True)
|
||
return Grid(material = np.where(threshold < Grid._minimal_surface[surface](x,y,z),materials[1],materials[0]),
|
||
size = size,
|
||
comments = util.execution_stamp('Grid','from_minimal_surface'),
|
||
)
|
||
|
||
|
||
def save(self,fname,compress=True):
|
||
"""
|
||
Save as VTK image data file.
|
||
|
||
Parameters
|
||
----------
|
||
fname : str or pathlib.Path
|
||
Filename to write. Valid extension is .vti, it will be appended if not given.
|
||
compress : bool, optional
|
||
Compress with zlib algorithm. Defaults to True.
|
||
|
||
"""
|
||
v = VTK.from_image_data(self.cells,self.size,self.origin)
|
||
v.add(self.material.flatten(order='F'),'material')
|
||
v.add_comments(self.comments)
|
||
|
||
v.save(fname if str(fname).endswith('.vti') else str(fname)+'.vti',parallel=False,compress=compress)
|
||
|
||
|
||
def save_ASCII(self,fname):
|
||
"""
|
||
Save as geom file.
|
||
|
||
Storing geometry files in ASCII format is deprecated.
|
||
This function will be removed in a future version of DAMASK.
|
||
|
||
Parameters
|
||
----------
|
||
fname : str or file handle
|
||
Geometry file to write with extension '.geom'.
|
||
compress : bool, optional
|
||
Compress geometry with 'x of y' and 'a to b'.
|
||
|
||
"""
|
||
warnings.warn('Support for ASCII-based geom format will be removed in DAMASK 3.0.0', DeprecationWarning,2)
|
||
header = [f'{len(self.comments)+4} header'] + self.comments \
|
||
+ ['grid a {} b {} c {}'.format(*self.cells),
|
||
'size x {} y {} z {}'.format(*self.size),
|
||
'origin x {} y {} z {}'.format(*self.origin),
|
||
'homogenization 1',
|
||
]
|
||
|
||
format_string = '%g' if self.material.dtype in np.sctypes['float'] else \
|
||
'%{}i'.format(1+int(np.floor(np.log10(np.nanmax(self.material)))))
|
||
np.savetxt(fname,
|
||
self.material.reshape([self.cells[0],np.prod(self.cells[1:])],order='F').T,
|
||
header='\n'.join(header), fmt=format_string, comments='')
|
||
|
||
|
||
def show(self):
|
||
"""Show on screen."""
|
||
VTK.from_rectilinear_grid(self.cells,self.size,self.origin).show()
|
||
|
||
|
||
def add_primitive(self,dimension,center,exponent,
|
||
fill=None,R=Rotation(),inverse=False,periodic=True):
|
||
"""
|
||
Insert a primitive geometric object at a given position.
|
||
|
||
Parameters
|
||
----------
|
||
dimension : int or float numpy.ndarray of shape (3)
|
||
Dimension (diameter/side length) of the primitive. If given as
|
||
integers, cell centers are addressed.
|
||
If given as floats, coordinates are addressed.
|
||
center : int or float numpy.ndarray of shape (3)
|
||
Center of the primitive. If given as integers, cell centers are addressed.
|
||
If given as floats, coordinates in space are addressed.
|
||
exponent : numpy.ndarray of shape (3) or float
|
||
Exponents for the three axes.
|
||
0 gives octahedron (ǀxǀ^(2^0) + ǀyǀ^(2^0) + ǀzǀ^(2^0) < 1)
|
||
1 gives sphere (ǀxǀ^(2^1) + ǀyǀ^(2^1) + ǀzǀ^(2^1) < 1)
|
||
fill : int, optional
|
||
Fill value for primitive. Defaults to material.max()+1.
|
||
R : damask.Rotation, optional
|
||
Rotation of primitive. Defaults to no rotation.
|
||
inverse : Boolean, optional
|
||
Retain original materials within primitive and fill outside.
|
||
Defaults to False.
|
||
periodic : Boolean, optional
|
||
Assume grid to be periodic. Defaults to True.
|
||
|
||
Returns
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
Examples
|
||
--------
|
||
Add a sphere at the center.
|
||
|
||
>>> import numpy as np
|
||
>>> import damask
|
||
>>> g = damask.Grid(np.zeros([64]*3,int), np.ones(3)*1e-4)
|
||
>>> g.add_primitive(np.ones(3)*5e-5,np.ones(3)*5e-5,1)
|
||
cells a b c: 64 x 64 x 64
|
||
size x y z: 0.0001 x 0.0001 x 0.0001
|
||
origin x y z: 0.0 0.0 0.0
|
||
# materials: 2
|
||
|
||
Add a cube at the origin.
|
||
|
||
>>> import numpy as np
|
||
>>> import damask
|
||
>>> g = damask.Grid(np.zeros([64]*3,int), np.ones(3)*1e-4)
|
||
>>> g.add_primitive(np.ones(3,int)*32,np.zeros(3),np.inf)
|
||
cells a b c: 64 x 64 x 64
|
||
size x y z: 0.0001 x 0.0001 x 0.0001
|
||
origin x y z: 0.0 0.0 0.0
|
||
# materials: 2
|
||
|
||
"""
|
||
# radius and center
|
||
r = np.array(dimension)/2.0*self.size/self.cells if np.array(dimension).dtype in np.sctypes['int'] else \
|
||
np.array(dimension)/2.0
|
||
c = (np.array(center) + .5)*self.size/self.cells if np.array(center).dtype in np.sctypes['int'] else \
|
||
(np.array(center) - self.origin)
|
||
|
||
coords = grid_filters.coordinates0_point(self.cells,self.size,
|
||
-(0.5*(self.size + (self.size/self.cells
|
||
if np.array(center).dtype in np.sctypes['int'] else
|
||
0)) if periodic else c))
|
||
coords_rot = R.broadcast_to(tuple(self.cells))@coords
|
||
|
||
with np.errstate(all='ignore'):
|
||
mask = np.sum(np.power(coords_rot/r,2.0**np.array(exponent)),axis=-1) > 1.0
|
||
|
||
if periodic: # translate back to center
|
||
mask = np.roll(mask,((c/self.size-0.5)*self.cells).round().astype(int),(0,1,2))
|
||
|
||
return Grid(material = np.where(np.logical_not(mask) if inverse else mask,
|
||
self.material,
|
||
np.nanmax(self.material)+1 if fill is None else fill),
|
||
size = self.size,
|
||
origin = self.origin,
|
||
comments = self.comments+[util.execution_stamp('Grid','add_primitive')],
|
||
)
|
||
|
||
|
||
def mirror(self,directions,reflect=False):
|
||
"""
|
||
Mirror grid along given directions.
|
||
|
||
Parameters
|
||
----------
|
||
directions : iterable containing str
|
||
Direction(s) along which the grid is mirrored.
|
||
Valid entries are 'x', 'y', 'z'.
|
||
reflect : bool, optional
|
||
Reflect (include) outermost layers. Defaults to False.
|
||
|
||
Returns
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
Examples
|
||
--------
|
||
Mirror along x- and y-direction.
|
||
|
||
>>> import numpy as np
|
||
>>> import damask
|
||
>>> g = damask.Grid(np.zeros([32]*3,int), np.ones(3)*1e-4)
|
||
>>> g.mirror('xy',True)
|
||
cells a b c: 64 x 64 x 32
|
||
size x y z: 0.0002 x 0.0002 x 0.0001
|
||
origin x y z: 0.0 0.0 0.0
|
||
# materials: 1
|
||
|
||
"""
|
||
valid = ['x','y','z']
|
||
if not set(directions).issubset(valid):
|
||
raise ValueError(f'invalid direction {set(directions).difference(valid)} specified')
|
||
|
||
limits = [None,None] if reflect else [-2,0]
|
||
mat = self.material.copy()
|
||
|
||
if 'x' in directions:
|
||
mat = np.concatenate([mat,mat[limits[0]:limits[1]:-1,:,:]],0)
|
||
if 'y' in directions:
|
||
mat = np.concatenate([mat,mat[:,limits[0]:limits[1]:-1,:]],1)
|
||
if 'z' in directions:
|
||
mat = np.concatenate([mat,mat[:,:,limits[0]:limits[1]:-1]],2)
|
||
|
||
return Grid(material = mat,
|
||
size = self.size/self.cells*np.asarray(mat.shape),
|
||
origin = self.origin,
|
||
comments = self.comments+[util.execution_stamp('Grid','mirror')],
|
||
)
|
||
|
||
|
||
def flip(self,directions):
|
||
"""
|
||
Flip grid along given directions.
|
||
|
||
Parameters
|
||
----------
|
||
directions : iterable containing str
|
||
Direction(s) along which the grid is flipped.
|
||
Valid entries are 'x', 'y', 'z'.
|
||
|
||
Returns
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
"""
|
||
valid = ['x','y','z']
|
||
if not set(directions).issubset(valid):
|
||
raise ValueError(f'invalid direction {set(directions).difference(valid)} specified')
|
||
|
||
mat = np.flip(self.material, (valid.index(d) for d in directions if d in valid))
|
||
|
||
return Grid(material = mat,
|
||
size = self.size,
|
||
origin = self.origin,
|
||
comments = self.comments+[util.execution_stamp('Grid','flip')],
|
||
)
|
||
|
||
|
||
def scale(self,cells,periodic=True):
|
||
"""
|
||
Scale grid to new cells.
|
||
|
||
Parameters
|
||
----------
|
||
cells : numpy.ndarray of shape (3)
|
||
Number of cells in x,y,z direction.
|
||
periodic : Boolean, optional
|
||
Assume grid to be periodic. Defaults to True.
|
||
|
||
Returns
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
Examples
|
||
--------
|
||
Double resolution.
|
||
|
||
>>> import numpy as np
|
||
>>> import damask
|
||
>>> g = damask.Grid(np.zeros([32]*3,int),np.ones(3)*1e-4)
|
||
>>> g.scale(g.cells*2)
|
||
cells a b c: 64 x 64 x 64
|
||
size x y z: 0.0001 x 0.0001 x 0.0001
|
||
origin x y z: 0.0 0.0 0.0
|
||
# materials: 1
|
||
|
||
"""
|
||
return Grid(material = ndimage.interpolation.zoom(
|
||
self.material,
|
||
cells/self.cells,
|
||
output=self.material.dtype,
|
||
order=0,
|
||
mode=('wrap' if periodic else 'nearest'),
|
||
prefilter=False
|
||
),
|
||
size = self.size,
|
||
origin = self.origin,
|
||
comments = self.comments+[util.execution_stamp('Grid','scale')],
|
||
)
|
||
|
||
|
||
def clean(self,stencil=3,selection=None,periodic=True):
|
||
"""
|
||
Smooth grid by selecting most frequent material index within given stencil at each location.
|
||
|
||
Parameters
|
||
----------
|
||
stencil : int, optional
|
||
Size of smoothing stencil.
|
||
selection : list, optional
|
||
Field values that can be altered. Defaults to all.
|
||
periodic : Boolean, optional
|
||
Assume grid to be periodic. Defaults to True.
|
||
|
||
Returns
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
"""
|
||
def mostFrequent(arr,selection=None):
|
||
me = arr[arr.size//2]
|
||
if selection is None or me in selection:
|
||
unique, inverse = np.unique(arr, return_inverse=True)
|
||
return unique[np.argmax(np.bincount(inverse))]
|
||
else:
|
||
return me
|
||
|
||
return Grid(material = ndimage.filters.generic_filter(
|
||
self.material,
|
||
mostFrequent,
|
||
size=(stencil if selection is None else stencil//2*2+1,)*3,
|
||
mode=('wrap' if periodic else 'nearest'),
|
||
extra_keywords=dict(selection=selection),
|
||
).astype(self.material.dtype),
|
||
size = self.size,
|
||
origin = self.origin,
|
||
comments = self.comments+[util.execution_stamp('Grid','clean')],
|
||
)
|
||
|
||
|
||
def renumber(self):
|
||
"""
|
||
Renumber sorted material indices as 0,...,N-1.
|
||
|
||
Returns
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
"""
|
||
_,renumbered = np.unique(self.material,return_inverse=True)
|
||
|
||
return Grid(material = renumbered.reshape(self.cells),
|
||
size = self.size,
|
||
origin = self.origin,
|
||
comments = self.comments+[util.execution_stamp('Grid','renumber')],
|
||
)
|
||
|
||
|
||
def rotate(self,R,fill=None):
|
||
"""
|
||
Rotate grid (pad if required).
|
||
|
||
Parameters
|
||
----------
|
||
R : damask.Rotation
|
||
Rotation to apply to the grid.
|
||
fill : int or float, optional
|
||
Material index to fill the corners. Defaults to material.max() + 1.
|
||
|
||
Returns
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
"""
|
||
if fill is None: fill = np.nanmax(self.material) + 1
|
||
dtype = float if isinstance(fill,float) or self.material.dtype in np.sctypes['float'] else int
|
||
|
||
material = self.material
|
||
# These rotations are always applied in the reference coordinate system, i.e. (z,x,z) not (z,x',z'')
|
||
# see https://www.cs.utexas.edu/~theshark/courses/cs354/lectures/cs354-14.pdf
|
||
for angle,axes in zip(R.as_Euler_angles(degrees=True)[::-1], [(0,1),(1,2),(0,1)]):
|
||
material_temp = ndimage.rotate(material,angle,axes,order=0,prefilter=False,output=dtype,cval=fill)
|
||
# avoid scipy interpolation errors for rotations close to multiples of 90°
|
||
material = material_temp if np.prod(material_temp.shape) != np.prod(material.shape) else \
|
||
np.rot90(material,k=np.rint(angle/90.).astype(int),axes=axes)
|
||
|
||
origin = self.origin-(np.asarray(material.shape)-self.cells)*.5 * self.size/self.cells
|
||
|
||
return Grid(material = material,
|
||
size = self.size/self.cells*np.asarray(material.shape),
|
||
origin = origin,
|
||
comments = self.comments+[util.execution_stamp('Grid','rotate')],
|
||
)
|
||
|
||
|
||
def canvas(self,cells=None,offset=None,fill=None):
|
||
"""
|
||
Crop or enlarge/pad grid.
|
||
|
||
Parameters
|
||
----------
|
||
cells : numpy.ndarray of shape (3)
|
||
Number of cells x,y,z direction.
|
||
offset : numpy.ndarray of shape (3)
|
||
Offset (measured in cells) from old to new grid [0,0,0].
|
||
fill : int or float, optional
|
||
Material index to fill the background. Defaults to material.max() + 1.
|
||
|
||
Returns
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
Examples
|
||
--------
|
||
Remove 1/2 of the microstructure in z-direction.
|
||
|
||
>>> import numpy as np
|
||
>>> import damask
|
||
>>> g = damask.Grid(np.zeros([32]*3,int),np.ones(3)*1e-4)
|
||
>>> g.canvas(np.array([32,32,16],int))
|
||
cells a b c: 33 x 32 x 16
|
||
size x y z: 0.0001 x 0.0001 x 5e-05
|
||
origin x y z: 0.0 0.0 0.0
|
||
# materials: 1
|
||
|
||
"""
|
||
if offset is None: offset = 0
|
||
if fill is None: fill = np.nanmax(self.material) + 1
|
||
dtype = float if int(fill) != fill or self.material.dtype in np.sctypes['float'] else int
|
||
|
||
canvas = np.full(self.cells if cells is None else cells,fill,dtype)
|
||
|
||
LL = np.clip( offset, 0,np.minimum(self.cells, cells+offset))
|
||
UR = np.clip( offset+cells, 0,np.minimum(self.cells, cells+offset))
|
||
ll = np.clip(-offset, 0,np.minimum( cells,self.cells-offset))
|
||
ur = np.clip(-offset+self.cells,0,np.minimum( cells,self.cells-offset))
|
||
|
||
canvas[ll[0]:ur[0],ll[1]:ur[1],ll[2]:ur[2]] = self.material[LL[0]:UR[0],LL[1]:UR[1],LL[2]:UR[2]]
|
||
|
||
return Grid(material = canvas,
|
||
size = self.size/self.cells*np.asarray(canvas.shape),
|
||
origin = self.origin+offset*self.size/self.cells,
|
||
comments = self.comments+[util.execution_stamp('Grid','canvas')],
|
||
)
|
||
|
||
|
||
def substitute(self,from_material,to_material):
|
||
"""
|
||
Substitute material indices.
|
||
|
||
Parameters
|
||
----------
|
||
from_material : iterable of ints
|
||
Material indices to be substituted.
|
||
to_material : iterable of ints
|
||
New material indices.
|
||
|
||
Returns
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
"""
|
||
def mp(entry,mapper):
|
||
return mapper[entry] if entry in mapper else entry
|
||
|
||
mp = np.vectorize(mp)
|
||
mapper = dict(zip(from_material,to_material))
|
||
|
||
return Grid(material = mp(self.material,mapper).reshape(self.cells),
|
||
size = self.size,
|
||
origin = self.origin,
|
||
comments = self.comments+[util.execution_stamp('Grid','substitute')],
|
||
)
|
||
|
||
|
||
def sort(self):
|
||
"""
|
||
Sort material indices such that min(material) is located at (0,0,0).
|
||
|
||
Returns
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
"""
|
||
a = self.material.flatten(order='F')
|
||
from_ma = pd.unique(a)
|
||
sort_idx = np.argsort(from_ma)
|
||
ma = np.unique(a)[sort_idx][np.searchsorted(from_ma,a,sorter = sort_idx)]
|
||
|
||
return Grid(material = ma.reshape(self.cells,order='F'),
|
||
size = self.size,
|
||
origin = self.origin,
|
||
comments = self.comments+[util.execution_stamp('Grid','sort')],
|
||
)
|
||
|
||
|
||
def vicinity_offset(self,vicinity=1,offset=None,trigger=[],periodic=True):
|
||
"""
|
||
Offset material index of points in the vicinity of xxx.
|
||
|
||
Different from themselves (or listed as triggers) within a given (cubic) vicinity,
|
||
i.e. within the region close to a grain/phase boundary.
|
||
ToDo: use include/exclude as in seeds.from_grid
|
||
|
||
Parameters
|
||
----------
|
||
vicinity : int, optional
|
||
Voxel distance checked for presence of other materials.
|
||
Defaults to 1.
|
||
offset : int, optional
|
||
Offset (positive or negative) to tag material indices,
|
||
defaults to material.max()+1.
|
||
trigger : list of ints, optional
|
||
List of material indices that trigger a change.
|
||
Defaults to [], meaning that any different neighbor triggers a change.
|
||
periodic : Boolean, optional
|
||
Assume grid to be periodic. Defaults to True.
|
||
|
||
Returns
|
||
-------
|
||
updated : damask.Grid
|
||
Updated grid-based geometry.
|
||
|
||
"""
|
||
def tainted_neighborhood(stencil,trigger):
|
||
|
||
me = stencil[stencil.shape[0]//2]
|
||
return np.any(stencil != me if len(trigger) == 0 else
|
||
np.in1d(stencil,np.array(list(set(trigger) - {me}))))
|
||
|
||
offset_ = np.nanmax(self.material)+1 if offset is None else offset
|
||
mask = ndimage.filters.generic_filter(self.material,
|
||
tainted_neighborhood,
|
||
size=1+2*vicinity,
|
||
mode='wrap' if periodic else 'nearest',
|
||
extra_keywords={'trigger':trigger})
|
||
|
||
return Grid(material = np.where(mask, self.material + offset_,self.material),
|
||
size = self.size,
|
||
origin = self.origin,
|
||
comments = self.comments+[util.execution_stamp('Grid','vicinity_offset')],
|
||
)
|
||
|
||
|
||
def get_grain_boundaries(self,periodic=True,directions='xyz'):
|
||
"""
|
||
Create VTK unstructured grid containing grain boundaries.
|
||
|
||
Parameters
|
||
----------
|
||
periodic : Boolean, optional
|
||
Assume grid to be periodic. Defaults to True.
|
||
directions : iterable containing str, optional
|
||
Direction(s) along which the boundaries are determined.
|
||
Valid entries are 'x', 'y', 'z'. Defaults to 'xyz'.
|
||
|
||
Returns
|
||
-------
|
||
grain_boundaries : damask.VTK
|
||
VTK-based geometry of grain boundary network.
|
||
|
||
"""
|
||
valid = ['x','y','z']
|
||
if not set(directions).issubset(valid):
|
||
raise ValueError(f'invalid direction {set(directions).difference(valid)} specified')
|
||
|
||
o = [[0, self.cells[0]+1, np.prod(self.cells[:2]+1)+self.cells[0]+1, np.prod(self.cells[:2]+1)],
|
||
[0, np.prod(self.cells[:2]+1), np.prod(self.cells[:2]+1)+1, 1],
|
||
[0, 1, self.cells[0]+1+1, self.cells[0]+1]] # offset for connectivity
|
||
|
||
connectivity = []
|
||
for i,d in enumerate(['x','y','z']):
|
||
if d not in directions: continue
|
||
mask = self.material != np.roll(self.material,1,i)
|
||
for j in [0,1,2]:
|
||
mask = np.concatenate((mask,np.take(mask,[0],j)*(i==j)),j)
|
||
if i == 0 and not periodic: mask[0,:,:] = mask[-1,:,:] = False
|
||
if i == 1 and not periodic: mask[:,0,:] = mask[:,-1,:] = False
|
||
if i == 2 and not periodic: mask[:,:,0] = mask[:,:,-1] = False
|
||
|
||
base_nodes = np.argwhere(mask.flatten(order='F')).reshape(-1,1)
|
||
connectivity.append(np.block([base_nodes + o[i][k] for k in range(4)]))
|
||
|
||
coords = grid_filters.coordinates0_node(self.cells,self.size,self.origin).reshape(-1,3,order='F')
|
||
return VTK.from_unstructured_grid(coords,np.vstack(connectivity),'QUAD')
|