#!/usr/bin/env python3 import os import sys import random from optparse import OptionParser,OptionGroup import numpy as np from scipy import spatial import damask scriptName = os.path.splitext(os.path.basename(__file__))[0] scriptID = ' '.join([scriptName,damask.version]) def kdtree_search(cloud, queryPoints): """Find distances to nearest neighbor among cloud (N,d) for each of the queryPoints (n,d).""" n = queryPoints.shape[0] distances = np.zeros(n,dtype=float) tree = spatial.cKDTree(cloud) for i in range(n): distances[i], index = tree.query(queryPoints[i]) return distances # -------------------------------------------------------------------- # MAIN # -------------------------------------------------------------------- parser = OptionParser(option_class=damask.extendableOption, usage='%prog options', description = """ Distribute given number of points randomly within (a fraction of) the three-dimensional cube [0.0,0.0,0.0]--[1.0,1.0,1.0]. Reports positions with random crystal orientations in seeds file format to STDOUT. """, version = scriptID) parser.add_option('-N', dest = 'N', type = 'int', metavar = 'int', help = 'number of seed points [%default]') parser.add_option('-f', '--fraction', dest = 'fraction', type = 'float', nargs = 3, metavar = 'float float float', help='fractions along x,y,z of unit cube to fill %default') parser.add_option('-g', '--grid', dest = 'grid', type = 'int', nargs = 3, metavar = 'int int int', help='min a,b,c grid of hexahedral box %default') parser.add_option('-m', '--microstructure', dest = 'microstructure', type = 'int', metavar = 'int', help = 'first microstructure index [%default]') parser.add_option('-r', '--rnd', dest = 'randomSeed', type = 'int', metavar = 'int', help = 'seed of random number generator [%default]') group = OptionGroup(parser, "Laguerre Tessellation", "Parameters determining shape of weight distribution of seed points" ) group.add_option( '-w', '--weights', action = 'store_true', dest = 'weights', help = 'assign random weights to seed points for Laguerre tessellation [%default]') group.add_option( '--max', dest = 'max', type = 'float', metavar = 'float', help = 'max of uniform distribution for weights [%default]') group.add_option( '--mean', dest = 'mean', type = 'float', metavar = 'float', help = 'mean of normal distribution for weights [%default]') group.add_option( '--sigma', dest = 'sigma', type = 'float', metavar = 'float', help='standard deviation of normal distribution for weights [%default]') parser.add_option_group(group) group = OptionGroup(parser, "Selective Seeding", "More uniform distribution of seed points using Mitchell's Best Candidate Algorithm" ) group.add_option( '-s', '--selective', action = 'store_true', dest = 'selective', help = 'selective picking of seed points from random seed points') group.add_option( '--distance', dest = 'distance', type = 'float', metavar = 'float', help = 'minimum distance to next neighbor [%default]') group.add_option( '--numCandidates', dest = 'numCandidates', type = 'int', metavar = 'int', help = 'size of point group to select best distance from [%default]') parser.add_option_group(group) parser.set_defaults(randomSeed = None, grid = (16,16,16), fraction = (1.0,1.0,1.0), N = 20, weights = False, max = 0.0, mean = 0.2, sigma = 0.05, microstructure = 1, selective = False, distance = 0.2, numCandidates = 10, ) (options,filenames) = parser.parse_args() if filenames == []: filenames = [None] fraction = np.array(options.fraction) grid = np.array(options.grid) if options.randomSeed is None: options.randomSeed = int(os.urandom(4).hex(), 16) np.random.seed(options.randomSeed) # init random generators random.seed(options.randomSeed) for name in filenames: damask.util.report(scriptName,name) # --- sanity checks ------------------------------------------------------------------------- remarks = [] errors = [] if any(grid==0): errors.append('zero grid dimension for {}.'.format(', '.join([['a','b','c'][x] for x in np.where(grid == 0)[0]]))) if options.N > grid.prod()/10.: remarks.append('seed count exceeds 0.1 of grid points.') if options.selective and 4./3.*np.pi*(options.distance/2.)**3*options.N > 0.5: remarks.append('maximum recommended seed point count for given distance is {}'. format(int(3./8./np.pi/(options.distance/2.)**3))) if remarks != []: damask.util.croak(remarks) if errors != []: damask.util.croak(errors) sys.exit() # --- do work ------------------------------------------------------------------------------------ grainEuler = np.random.rand(3,options.N) # create random Euler triplets grainEuler[0,:] *= 360.0 # phi_1 is uniformly distributed grainEuler[1,:] = np.degrees(np.arccos(2*grainEuler[1,:]-1)) # cos(Phi) is uniformly distributed grainEuler[2,:] *= 360.0 # phi_2 is uniformly distributed if not options.selective: n = np.maximum(np.ones(3),np.array(grid*fraction), dtype=int,casting='unsafe') # find max grid indices within fraction meshgrid = np.meshgrid(*map(np.arange,n),indexing='ij') # create a meshgrid within fraction coords = np.vstack((meshgrid[0],meshgrid[1],meshgrid[2])).reshape(3,n.prod()).T # assemble list of 3D coordinates seeds = ((random.sample(list(coords),options.N)+np.random.random(options.N*3).reshape(options.N,3))\ / \ (n/fraction)).T # pick options.N of those, rattle position, # and rescale to fall within fraction else: seeds = np.zeros((options.N,3),dtype=float) # seed positions array seeds[0] = np.random.random(3)*grid/max(grid) i = 1 # start out with one given point if i%(options.N/100.) < 1: damask.util.croak('.',False) while i < options.N: candidates = np.random.random(options.numCandidates*3).reshape(options.numCandidates,3) distances = kdtree_search(seeds[:i],candidates) best = distances.argmax() if distances[best] > options.distance: # require minimum separation seeds[i] = candidates[best] # maximum separation to existing point cloud i += 1 if i%(options.N/100.) < 1: damask.util.croak('.',False) damask.util.croak('') seeds = seeds.T # prepare shape for stacking if options.weights: weights = [np.random.uniform(low = 0, high = options.max, size = options.N)] if options.max > 0.0 \ else [np.random.normal(loc = options.mean, scale = options.sigma, size = options.N)] data = np.transpose(np.vstack(tuple([seeds, grainEuler, np.arange(options.microstructure,options.microstructure + options.N), ] + (weights if options.weights else []) ))) comments = [scriptID + ' ' + ' '.join(sys.argv[1:]), 'grid\ta {}\tb {}\tc {}'.format(*grid), 'randomSeed\t{}'.format(options.randomSeed), ] shapes = {'pos':(3,),'euler':(3,),'microstructure':(1,)} if options.weights: shapes['weight'] = (1,) table = damask.Table(data,shapes,comments) table.to_ASCII(sys.stdout if name is None else name)