Source code for damask._grid

import os
import copy
import warnings
import multiprocessing as mp
from functools import partial

import numpy as np
import pandas as pd
import h5py
from scipy import ndimage, spatial

from . import VTK
from . import util
from . import grid_filters
from . import Rotation


[docs]class Grid: """ Geometry definition for grid solvers. Create and manipulate geometry definitions for storage as VTK image data files ('.vti' extension). A grid contains the material ID (referring to the entry in 'material.yaml') and the physical size. """ def __init__(self,material,size,origin=[0.0,0.0,0.0],comments=[]): """ New geometry definition for grid solvers. Parameters ---------- material : numpy.ndarray of shape (:,:,:) Material indices. The shape of the material array defines the number of cells. size : list or numpy.ndarray of shape (3) Physical size of grid in meter. origin : list or numpy.ndarray of shape (3), optional Coordinates of grid origin in meter. comments : list of str, optional Comments, e.g. history of operations. """ self.material = material self.size = size self.origin = origin self.comments = comments def __repr__(self): """Basic information on grid definition.""" mat_min = np.nanmin(self.material) mat_max = np.nanmax(self.material) mat_N = self.N_materials return util.srepr([ f'cells a b c: {util.srepr(self.cells, " x ")}', f'size x y z: {util.srepr(self.size, " x ")}', f'origin x y z: {util.srepr(self.origin," ")}', f'# materials: {mat_N}' + ('' if mat_min == 0 and mat_max+1 == mat_N else f' (min: {mat_min}, max: {mat_max})') ]) def __copy__(self): """Create deep copy.""" return copy.deepcopy(self) copy = __copy__ def __eq__(self,other): """ Test equality of other. Parameters ---------- other : damask.Grid Grid to compare self against. """ return (np.allclose(other.size,self.size) and np.allclose(other.origin,self.origin) and np.all(other.cells == self.cells) and np.all(other.material == self.material)) @property def material(self): """Material indices.""" return self._material @material.setter def material(self,material): if len(material.shape) != 3: raise ValueError(f'invalid material shape {material.shape}') elif material.dtype not in np.sctypes['float'] + np.sctypes['int']: raise TypeError(f'invalid material data type {material.dtype}') else: self._material = np.copy(material) if self.material.dtype in np.sctypes['float'] and \ np.all(self.material == self.material.astype(int).astype(float)): self._material = self.material.astype(int) @property def size(self): """Physical size of grid in meter.""" return self._size @size.setter def size(self,size): if len(size) != 3 or any(np.array(size) < 0): raise ValueError(f'invalid size {size}') else: self._size = np.array(size) @property def origin(self): """Coordinates of grid origin in meter.""" return self._origin @origin.setter def origin(self,origin): if len(origin) != 3: raise ValueError(f'invalid origin {origin}') else: self._origin = np.array(origin) @property def comments(self): """Comments, e.g. history of operations.""" return self._comments @comments.setter def comments(self,comments): self._comments = [str(c) for c in comments] if isinstance(comments,list) else [str(comments)] @property def cells(self): """Number of cells in x,y,z direction.""" return np.asarray(self.material.shape) @property def N_materials(self): """Number of (unique) material indices within grid.""" return np.unique(self.material).size
[docs] @staticmethod def load(fname): """ Load from VTK image data file. Parameters ---------- fname : str or or pathlib.Path Grid file to read. Valid extension is .vti, which will be appended if not given. Returns ------- loaded : damask.Grid Grid-based geometry from file. """ v = VTK.load(fname if str(fname).endswith(('.vti','.vtr')) else str(fname)+'.vti') # compatibility hack comments = v.get_comments() cells = np.array(v.vtk_data.GetDimensions())-1 bbox = np.array(v.vtk_data.GetBounds()).reshape(3,2).T return Grid(material = v.get('material').reshape(cells,order='F'), size = bbox[1] - bbox[0], origin = bbox[0], comments=comments)
[docs] @staticmethod def load_ASCII(fname): """ Load from geom file. Storing geometry files in ASCII format is deprecated. This function will be removed in a future version of DAMASK. Parameters ---------- fname : str, pathlib.Path, or file handle Geometry file to read. Returns ------- loaded : damask.Grid Grid-based geometry from file. """ warnings.warn('Support for ASCII-based geom format will be removed in DAMASK 3.1.0', DeprecationWarning,2) try: f = open(fname) except TypeError: f = fname f.seek(0) try: header_length,keyword = f.readline().split()[:2] header_length = int(header_length) except ValueError: header_length,keyword = (-1, 'invalid') if not keyword.startswith('head') or header_length < 3: raise TypeError('header length information missing or invalid') comments = [] content = f.readlines() for i,line in enumerate(content[:header_length]): items = line.split('#')[0].lower().strip().split() key = items[0] if items else '' if key == 'grid': cells = np.array([ int(dict(zip(items[1::2],items[2::2]))[i]) for i in ['a','b','c']]) elif key == 'size': size = np.array([float(dict(zip(items[1::2],items[2::2]))[i]) for i in ['x','y','z']]) elif key == 'origin': origin = np.array([float(dict(zip(items[1::2],items[2::2]))[i]) for i in ['x','y','z']]) else: comments.append(line.strip()) material = np.empty(cells.prod()) # initialize as flat array i = 0 for line in content[header_length:]: items = line.split('#')[0].split() if len(items) == 3: if items[1].lower() == 'of': items = np.ones(int(items[0]))*float(items[2]) elif items[1].lower() == 'to': items = np.linspace(int(items[0]),int(items[2]), abs(int(items[2])-int(items[0]))+1,dtype=float) else: items = list(map(float,items)) else: items = list(map(float,items)) material[i:i+len(items)] = items i += len(items) if i != cells.prod(): raise TypeError(f'invalid file: expected {cells.prod()} entries, found {i}') if not np.any(np.mod(material,1) != 0.0): # no float present material = material.astype('int') - (1 if material.min() > 0 else 0) return Grid(material.reshape(cells,order='F'),size,origin,comments)
[docs] @staticmethod def load_Neper(fname): """ Load from Neper VTK file. Parameters ---------- fname : str, pathlib.Path, or file handle Geometry file to read. Returns ------- loaded : damask.Grid Grid-based geometry from file. """ v = VTK.load(fname,'vtkImageData') cells = np.array(v.vtk_data.GetDimensions())-1 bbox = np.array(v.vtk_data.GetBounds()).reshape(3,2).T return Grid(v.get('MaterialId').reshape(cells,order='F').astype('int32',casting='unsafe') - 1, bbox[1] - bbox[0], bbox[0], util.execution_stamp('Grid','load_Neper'))
[docs] @staticmethod def load_DREAM3D(fname, feature_IDs=None,cell_data=None, phases='Phases',Euler_angles='EulerAngles', base_group=None): """ Load DREAM.3D (HDF5) file. Data in DREAM.3D files can be stored per cell ('CellData') and/or per grain ('Grain Data'). Per default, cell-wise data is assumed. damask.ConfigMaterial.load_DREAM3D gives the corresponding material definition. Parameters ---------- fname : str Filename of the DREAM.3D (HDF5) file. feature_IDs : str Name of the dataset containing the mapping between cells and grain-wise data. Defaults to 'None', in which case cell-wise data is used. cell_data : str Name of the group (folder) containing cell-wise data. Defaults to None in wich case it is automatically detected. phases : str Name of the dataset containing the phase ID. It is not used for grain-wise data, i.e. when feature_IDs is not None. Defaults to 'Phases'. Euler_angles : str Name of the dataset containing the crystallographic orientation as Euler angles in radians It is not used for grain-wise data, i.e. when feature_IDs is not None. Defaults to 'EulerAngles'. base_group : str Path to the group (folder) that contains geometry (_SIMPL_GEOMETRY), and grain- or cell-wise data. Defaults to None, in which case it is set as the path that contains _SIMPL_GEOMETRY/SPACING. Returns ------- loaded : damask.Grid Grid-based geometry from file. """ b = util.DREAM3D_base_group(fname) if base_group is None else base_group c = util.DREAM3D_cell_data_group(fname) if cell_data is None else cell_data f = h5py.File(fname, 'r') cells = f['/'.join([b,'_SIMPL_GEOMETRY','DIMENSIONS'])][()] size = f['/'.join([b,'_SIMPL_GEOMETRY','SPACING'])] * cells origin = f['/'.join([b,'_SIMPL_GEOMETRY','ORIGIN'])][()] if feature_IDs is None: phase = f['/'.join([b,c,phases])][()].reshape(-1,1) O = Rotation.from_Euler_angles(f['/'.join([b,c,Euler_angles])]).as_quaternion().reshape(-1,4) # noqa unique,unique_inverse = np.unique(np.hstack([O,phase]),return_inverse=True,axis=0) ma = np.arange(cells.prod()) if len(unique) == cells.prod() else \ np.arange(unique.size)[np.argsort(pd.unique(unique_inverse))][unique_inverse] else: ma = f['/'.join([b,c,feature_IDs])][()].flatten() return Grid(ma.reshape(cells,order='F'),size,origin,util.execution_stamp('Grid','load_DREAM3D'))
[docs] @staticmethod def from_table(table,coordinates,labels): """ Create grid from ASCII table. Parameters ---------- table : damask.Table Table that contains material information. coordinates : str Label of the vector column containing the spatial coordinates. Need to be ordered (1./x fast, 3./z slow). labels : str or list of str Label(s) of the columns containing the material definition. Each unique combination of values results in one material ID. Returns ------- new : damask.Grid Grid-based geometry from values in table. """ cells,size,origin = grid_filters.cellsSizeOrigin_coordinates0_point(table.get(coordinates)) labels_ = [labels] if isinstance(labels,str) else labels unique,unique_inverse = np.unique(np.hstack([table.get(l) for l in labels_]),return_inverse=True,axis=0) ma = np.arange(cells.prod()) if len(unique) == cells.prod() else \ np.arange(unique.size)[np.argsort(pd.unique(unique_inverse))][unique_inverse] return Grid(ma.reshape(cells,order='F'),size,origin,util.execution_stamp('Grid','from_table'))
@staticmethod def _find_closest_seed(seeds, weights, point): return np.argmin(np.sum((np.broadcast_to(point,(len(seeds),3))-seeds)**2,axis=1) - weights)
[docs] @staticmethod def from_Laguerre_tessellation(cells,size,seeds,weights,material=None,periodic=True): """ Create grid from Laguerre tessellation. Parameters ---------- cells : int numpy.ndarray of shape (3) Number of cells in x,y,z direction. size : list or numpy.ndarray of shape (3) Physical size of the grid in meter. seeds : numpy.ndarray of shape (:,3) Position of the seed points in meter. All points need to lay within the box. weights : numpy.ndarray of shape (seeds.shape[0]) Weights of the seeds. Setting all weights to 1.0 gives a standard Voronoi tessellation. material : numpy.ndarray of shape (seeds.shape[0]), optional Material ID of the seeds. Defaults to None, in which case materials are consecutively numbered. periodic : Boolean, optional Assume grid to be periodic. Defaults to True. Returns ------- new : damask.Grid Grid-based geometry from tessellation. """ if periodic: weights_p = np.tile(weights,27) # Laguerre weights (1,2,3,1,2,3,...,1,2,3) seeds_p = np.vstack((seeds -np.array([size[0],0.,0.]),seeds, seeds +np.array([size[0],0.,0.]))) seeds_p = np.vstack((seeds_p-np.array([0.,size[1],0.]),seeds_p,seeds_p+np.array([0.,size[1],0.]))) seeds_p = np.vstack((seeds_p-np.array([0.,0.,size[2]]),seeds_p,seeds_p+np.array([0.,0.,size[2]]))) else: weights_p = weights seeds_p = seeds coords = grid_filters.coordinates0_point(cells,size).reshape(-1,3) pool = mp.Pool(int(os.environ.get('OMP_NUM_THREADS',4))) result = pool.map_async(partial(Grid._find_closest_seed,seeds_p,weights_p), coords) pool.close() pool.join() material_ = np.array(result.get()).reshape(cells) if periodic: material_ %= len(weights) return Grid(material = material_ if material is None else material[material_], size = size, comments = util.execution_stamp('Grid','from_Laguerre_tessellation'), )
[docs] @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) ), }
[docs] @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'), )
[docs] 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)
[docs] 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 3.1.0', DeprecationWarning,2) header = [f'{len(self.comments)+4} header'] + self.comments \ + ['grid a {} b {} c {}'.format(*self.cells), 'size x {} y {} z {}'.format(*self.size), 'origin x {} y {} z {}'.format(*self.origin), 'homogenization 1', ] format_string = '%g' if self.material.dtype in np.sctypes['float'] else \ '%{}i'.format(1+int(np.floor(np.log10(np.nanmax(self.material))))) np.savetxt(fname, self.material.reshape([self.cells[0],np.prod(self.cells[1:])],order='F').T, header='\n'.join(header), fmt=format_string, comments='')
[docs] def show(self): """Show on screen.""" VTK.from_rectilinear_grid(self.cells,self.size,self.origin).show()
[docs] 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')], )
[docs] 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')], )
[docs] 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')], )
[docs] 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')], )
[docs] 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')], )
[docs] 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')], )
[docs] 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')], )
[docs] 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')], )
[docs] 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')], )
[docs] 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')], )
[docs] 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')], )
[docs] 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')