#!/usr/bin/env python2.7 # -*- coding: UTF-8 no BOM -*- import os,sys,math,random import numpy as np import damask from optparse import OptionParser,OptionGroup from scipy import spatial scriptName = os.path.splitext(os.path.basename(__file__))[0] scriptID = ' '.join([scriptName,damask.version]) # ------------------------------------------ aux functions --------------------------------- 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]') parser.add_option('--format', dest = 'format', type = 'string', metavar = 'string', help = 'output number format [auto]') 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 [%default]') group.add_option( '--force', action = 'store_true', dest = 'force', help = 'try selective picking despite large seed point number [%default]') 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, force = False, distance = 0.2, numCandidates = 10, format = None, ) (options,filenames) = parser.parse_args() options.fraction = np.array(options.fraction) options.grid = np.array(options.grid) gridSize = options.grid.prod() if options.randomSeed is None: options.randomSeed = int(os.urandom(4).encode('hex'), 16) np.random.seed(options.randomSeed) # init random generators random.seed(options.randomSeed) # --- loop over output files ------------------------------------------------------------------------- if filenames == []: filenames = [None] for name in filenames: try: table = damask.ASCIItable(outname = name, buffered = False) except: continue damask.util.report(scriptName,name) # --- sanity checks ------------------------------------------------------------------------- remarks = [] errors = [] if gridSize == 0: errors.append('zero grid dimension for {}.'.format(', '.join([['a','b','c'][x] for x in np.where(options.grid == 0)[0]]))) if options.N > gridSize/10.: errors.append('seed count exceeds 0.1 of grid points.') if options.selective and 4./3.*math.pi*(options.distance/2.)**3*options.N > 0.5: (remarks if options.force else errors).append('maximum recommended seed point count for given distance is {}.{}'. format(int(3./8./math.pi/(options.distance/2.)**3),'..'*options.force)) 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(options.grid*options.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(coords,options.N)+np.random.random(options.N*3).reshape(options.N,3))\ / \ (n/options.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)*options.grid/max(options.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)] else: weights = [] seeds = np.transpose(np.vstack(tuple([seeds, grainEuler, np.arange(options.microstructure, options.microstructure + options.N), ] + weights ))) # ------------------------------------------ assemble header --------------------------------------- table.info_clear() table.info_append([ scriptID + ' ' + ' '.join(sys.argv[1:]), "grid\ta {}\tb {}\tc {}".format(*options.grid), "microstructures\t{}".format(options.N), "randomSeed\t{}".format(options.randomSeed), ]) table.labels_clear() table.labels_append( ['{dim}_{label}'.format(dim = 1+k,label = 'pos') for k in range(3)] + ['{dim}_{label}'.format(dim = 1+k,label = 'euler') for k in range(3)] + ['microstructure'] + (['weight'] if options.weights else [])) table.head_write() table.output_flush() # --- write seeds information ------------------------------------------------------------ table.data = seeds table.data_writeArray(fmt = options.format) # --- output finalization -------------------------------------------------------------------------- table.close() # close ASCII table