Merge branch 'development' into unified-RK4-RKCK45

This commit is contained in:
Martin Diehl 2020-04-24 06:29:51 +02:00
commit 49963b9f04
21 changed files with 288 additions and 224 deletions

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@ -203,7 +203,6 @@ Post_OrientationConversion:
stage: postprocessing
script:
- OrientationConversion/test.py
- OrientationConversion/test2.py
except:
- master
- release

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@ -1 +1 @@
v2.0.3-2303-g2a6132b7
v2.0.3-2364-g62f7363a

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@ -33,7 +33,7 @@ for filename in options.filenames:
results = damask.Result(filename)
if not results.structured: continue
coords = damask.grid_filters.cell_coord0(results.grid,results.size,results.origin)
coords = damask.grid_filters.cell_coord0(results.grid,results.size,results.origin).reshape(-1,3,order='F')
N_digits = int(np.floor(np.log10(int(results.increments[-1][3:]))))+1
N_digits = 5 # hack to keep test intact

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@ -17,7 +17,7 @@ def volTetrahedron(coords):
"""
Return the volume of the tetrahedron with given vertices or sides.
Ifvertices are given they must be in a NumPy array with shape (4,3): the
If vertices are given they must be in a NumPy array with shape (4,3): the
position vectors of the 4 vertices in 3 dimensions; if the six sides are
given, they must be an array of length 6. If both are given, the sides
will be used in the calculation.
@ -67,14 +67,13 @@ def volumeMismatch(size,F,nodes):
(compatible) cube and determinant of deformation gradient at Fourier point.
"""
coords = np.empty([8,3])
vMismatch = np.empty(grid[::-1])
volInitial = size.prod()/grid.prod()
vMismatch = np.empty(F.shape[:3])
#--------------------------------------------------------------------------------------------------
# calculate actual volume and volume resulting from deformation gradient
for k in range(grid[2]):
for k in range(grid[0]):
for j in range(grid[1]):
for i in range(grid[0]):
for i in range(grid[2]):
coords[0,0:3] = nodes[k, j, i ,0:3]
coords[1,0:3] = nodes[k ,j, i+1,0:3]
coords[2,0:3] = nodes[k ,j+1,i+1,0:3]
@ -91,8 +90,7 @@ def volumeMismatch(size,F,nodes):
+ abs(volTetrahedron([coords[6,0:3],coords[4,0:3],coords[1,0:3],coords[5,0:3]])) \
+ abs(volTetrahedron([coords[6,0:3],coords[4,0:3],coords[1,0:3],coords[0,0:3]]))) \
/np.linalg.det(F[k,j,i,0:3,0:3])
return vMismatch/volInitial
return vMismatch/(size.prod()/grid.prod())
def shapeMismatch(size,F,nodes,centres):
@ -103,35 +101,34 @@ def shapeMismatch(size,F,nodes,centres):
the corners of reconstructed (combatible) volume element and the vectors calculated by deforming
the initial volume element with the current deformation gradient.
"""
coordsInitial = np.empty([8,3])
sMismatch = np.empty(grid[::-1])
sMismatch = np.empty(F.shape[:3])
#--------------------------------------------------------------------------------------------------
# initial positions
coordsInitial[0,0:3] = [-size[0]/grid[0],-size[1]/grid[1],-size[2]/grid[2]]
coordsInitial[1,0:3] = [+size[0]/grid[0],-size[1]/grid[1],-size[2]/grid[2]]
coordsInitial[2,0:3] = [+size[0]/grid[0],+size[1]/grid[1],-size[2]/grid[2]]
coordsInitial[3,0:3] = [-size[0]/grid[0],+size[1]/grid[1],-size[2]/grid[2]]
coordsInitial[4,0:3] = [-size[0]/grid[0],-size[1]/grid[1],+size[2]/grid[2]]
coordsInitial[5,0:3] = [+size[0]/grid[0],-size[1]/grid[1],+size[2]/grid[2]]
coordsInitial[6,0:3] = [+size[0]/grid[0],+size[1]/grid[1],+size[2]/grid[2]]
coordsInitial[7,0:3] = [-size[0]/grid[0],+size[1]/grid[1],+size[2]/grid[2]]
coordsInitial = coordsInitial/2.0
delta = size/grid*.5
coordsInitial = np.vstack((delta * np.array((-1,-1,-1)),
delta * np.array((+1,-1,-1)),
delta * np.array((+1,+1,-1)),
delta * np.array((-1,+1,-1)),
delta * np.array((-1,-1,+1)),
delta * np.array((+1,-1,+1)),
delta * np.array((+1,+1,+1)),
delta * np.array((-1,+1,+1))))
#--------------------------------------------------------------------------------------------------
# compare deformed original and deformed positions to actual positions
for k in range(grid[2]):
for k in range(grid[0]):
for j in range(grid[1]):
for i in range(grid[0]):
for i in range(grid[2]):
sMismatch[k,j,i] = \
+ np.linalg.norm(nodes[k, j, i ,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[0,0:3]))\
+ np.linalg.norm(nodes[k, j, i+1,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[1,0:3]))\
+ np.linalg.norm(nodes[k, j+1,i+1,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[2,0:3]))\
+ np.linalg.norm(nodes[k+1,j, i ,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[1,0:3]))\
+ np.linalg.norm(nodes[k+1,j+1,i ,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[2,0:3]))\
+ np.linalg.norm(nodes[k, j+1,i ,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[3,0:3]))\
+ np.linalg.norm(nodes[k+1,j, i ,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[4,0:3]))\
+ np.linalg.norm(nodes[k, j, i+1,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[4,0:3]))\
+ np.linalg.norm(nodes[k+1,j, i+1,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[5,0:3]))\
+ np.linalg.norm(nodes[k+1,j+1,i+1,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[6,0:3]))\
+ np.linalg.norm(nodes[k+1,j+1,i ,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[7,0:3]))
+ np.linalg.norm(nodes[k ,j+1,i+1,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[7,0:3]))
return sMismatch
@ -178,20 +175,20 @@ for name in filenames:
table = damask.Table.from_ASCII(StringIO(''.join(sys.stdin.read())) if name is None else name)
grid,size,origin = damask.grid_filters.cell_coord0_gridSizeOrigin(table.get(options.pos))
F = table.get(options.defgrad).reshape(grid[2],grid[1],grid[0],3,3)
F = table.get(options.defgrad).reshape(tuple(grid)+(-1,),order='F').reshape(tuple(grid)+(3,3))
nodes = damask.grid_filters.node_coord(size,F)
if options.shape:
centers = damask.grid_filters.cell_coord(size,F)
shapeMismatch = shapeMismatch( size,table.get(options.defgrad).reshape(grid[2],grid[1],grid[0],3,3),nodes,centers)
shapeMismatch = shapeMismatch(size,F,nodes,centers)
table.add('shapeMismatch(({}))'.format(options.defgrad),
shapeMismatch.reshape(-1,1),
shapeMismatch.reshape(-1,1,order='F'),
scriptID+' '+' '.join(sys.argv[1:]))
if options.volume:
volumeMismatch = volumeMismatch(size,table.get(options.defgrad).reshape(grid[2],grid[1],grid[0],3,3),nodes)
volumeMismatch = volumeMismatch(size,F,nodes)
table.add('volMismatch(({}))'.format(options.defgrad),
volumeMismatch.reshape(-1,1),
volumeMismatch.reshape(-1,1,order='F'),
scriptID+' '+' '.join(sys.argv[1:]))
table.to_ASCII(sys.stdout if name is None else name)

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@ -49,9 +49,10 @@ for name in filenames:
for label in options.labels:
field = table.get(label)
shape = (3,) if np.prod(field.shape)//np.prod(grid) == 3 else (3,3) # vector or tensor
field = field.reshape(np.append(grid[::-1],shape))
field = field.reshape(tuple(grid)+(-1,),order='F').reshape(tuple(grid)+shape)
curl = damask.grid_filters.curl(size,field)
table.add('curlFFT({})'.format(label),
damask.grid_filters.curl(size[::-1],field).reshape(-1,np.prod(shape)),
curl.reshape(tuple(grid)+(-1,)).reshape(-1,np.prod(shape),order='F'),
scriptID+' '+' '.join(sys.argv[1:]))
table.to_ASCII(sys.stdout if name is None else name)

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@ -5,8 +5,6 @@ import sys
from io import StringIO
from optparse import OptionParser
import numpy as np
import damask
@ -52,22 +50,22 @@ for name in filenames:
table = damask.Table.from_ASCII(StringIO(''.join(sys.stdin.read())) if name is None else name)
grid,size,origin = damask.grid_filters.cell_coord0_gridSizeOrigin(table.get(options.pos))
F = table.get(options.f).reshape(np.append(grid[::-1],(3,3)))
F = table.get(options.f).reshape(tuple(grid)+(-1,),order='F').reshape(tuple(grid)+(3,3))
if options.nodal:
table = damask.Table(damask.grid_filters.node_coord0(grid[::-1],size[::-1]).reshape(-1,3),
table = damask.Table(damask.grid_filters.node_coord0(grid,size).reshape(-1,3,order='F'),
{'pos':(3,)})
table.add('avg({}).{}'.format(options.f,options.pos),
damask.grid_filters.node_displacement_avg(size[::-1],F).reshape(-1,3),
damask.grid_filters.node_displacement_avg(size,F).reshape(-1,3,order='F'),
scriptID+' '+' '.join(sys.argv[1:]))
table.add('fluct({}).{}'.format(options.f,options.pos),
damask.grid_filters.node_displacement_fluct(size[::-1],F).reshape(-1,3),
damask.grid_filters.node_displacement_fluct(size,F).reshape(-1,3,order='F'),
scriptID+' '+' '.join(sys.argv[1:]))
table.to_ASCII(sys.stdout if name is None else os.path.splitext(name)[0]+'_nodal.txt')
else:
table.add('avg({}).{}'.format(options.f,options.pos),
damask.grid_filters.cell_displacement_avg(size[::-1],F).reshape(-1,3),
damask.grid_filters.cell_displacement_avg(size,F).reshape(-1,3,order='F'),
scriptID+' '+' '.join(sys.argv[1:]))
table.add('fluct({}).{}'.format(options.f,options.pos),
damask.grid_filters.cell_displacement_fluct(size[::-1],F).reshape(-1,3),
damask.grid_filters.cell_displacement_fluct(size,F).reshape(-1,3,order='F'),
scriptID+' '+' '.join(sys.argv[1:]))
table.to_ASCII(sys.stdout if name is None else name)

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@ -49,9 +49,10 @@ for name in filenames:
for label in options.labels:
field = table.get(label)
shape = (3,) if np.prod(field.shape)//np.prod(grid) == 3 else (3,3) # vector or tensor
field = field.reshape(np.append(grid[::-1],shape))
field = field.reshape(tuple(grid)+(-1,),order='F').reshape(tuple(grid)+shape)
div = damask.grid_filters.divergence(size,field)
table.add('divFFT({})'.format(label),
damask.grid_filters.divergence(size[::-1],field).reshape(-1,np.prod(shape)//3),
div.reshape(tuple(grid)+(-1,)).reshape(-1,np.prod(shape)//3,order='F'),
scriptID+' '+' '.join(sys.argv[1:]))
table.to_ASCII(sys.stdout if name is None else name)

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@ -49,9 +49,10 @@ for name in filenames:
for label in options.labels:
field = table.get(label)
shape = (1,) if np.prod(field.shape)//np.prod(grid) == 1 else (3,) # scalar or vector
field = field.reshape(np.append(grid[::-1],shape))
field = field.reshape(tuple(grid)+(-1,),order='F')
grad = damask.grid_filters.gradient(size,field)
table.add('gradFFT({})'.format(label),
damask.grid_filters.gradient(size[::-1],field).reshape(-1,np.prod(shape)*3),
grad.reshape(tuple(grid)+(-1,)).reshape(-1,np.prod(shape)*3,order='F'),
scriptID+' '+' '.join(sys.argv[1:]))
table.to_ASCII(sys.stdout if name is None else name)

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@ -91,7 +91,7 @@ for name in filenames:
table = damask.Table(averagedDown,table.shapes,table.comments)
coords = damask.grid_filters.cell_coord0(packedGrid,size,shift/packedGrid*size+origin)
table.set(options.pos, coords.reshape(-1,3))
table.set(options.pos, coords.reshape(-1,3,order='F'))
outname = os.path.join(os.path.dirname(name),prefix+os.path.basename(name))

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@ -59,13 +59,13 @@ for name in filenames:
packing = np.array(options.packing,'i')
outSize = grid*packing
data = table.data.values.reshape(tuple(grid)+(-1,))
blownUp = ndimage.interpolation.zoom(data,tuple(packing)+(1,),order=0,mode='nearest').reshape(outSize.prod(),-1)
data = table.data.values.reshape(tuple(grid)+(-1,),order='F')
blownUp = ndimage.interpolation.zoom(data,tuple(packing)+(1,),order=0,mode='nearest').reshape(outSize.prod(),-1,order='F')
table = damask.Table(blownUp,table.shapes,table.comments)
coords = damask.grid_filters.cell_coord0(outSize,size,origin)
table.set(options.pos,coords.reshape(-1,3))
table.set(options.pos,coords.reshape(-1,3,order='F'))
table.set('elem',np.arange(1,outSize.prod()+1))
outname = os.path.join(os.path.dirname(name),prefix+os.path.basename(name))

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@ -97,10 +97,10 @@ for name in filenames:
for col,dim in zip(columns,dims):
if options.unique:
s = set(map(tuple,table.data[:,col:col+dim])) # generate set of (unique) values
uniques = np.array(map(np.array,s)) # translate set to np.array
uniques = np.array(list(map(np.array,s))) # translate set to np.array
shuffler = dict(zip(s,np.random.permutation(len(s)))) # random permutation
table.data[:,col:col+dim] = uniques[np.array(map(lambda x: shuffler[tuple(x)],
table.data[:,col:col+dim]))] # fill table with mapped uniques
table.data[:,col:col+dim] = uniques[np.array(list(map(lambda x: shuffler[tuple(x)],
table.data[:,col:col+dim])))] # fill table with mapped uniques
else:
np.random.shuffle(table.data[:,col:col+dim]) # independently shuffle every row

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@ -24,22 +24,22 @@ def findClosestSeed(seeds, weights, point):
def Laguerre_tessellation(grid, size, seeds, weights, origin = np.zeros(3), periodic = True, cpus = 2):
if periodic:
weights_p = np.tile(weights,27).flatten(order='F') # Laguerre weights (1,2,3,1,2,3,...,1,2,3)
weights_p = np.tile(weights.squeeze(),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]])))
coords = damask.grid_filters.cell_coord0(grid*3,size*3,-origin-size).reshape(-1,3,order='F')
coords = damask.grid_filters.cell_coord0(grid*3,size*3,-origin-size).reshape(-1,3)
else:
weights_p = weights.flatten()
weights_p = weights.squeeze()
seeds_p = seeds
coords = damask.grid_filters.cell_coord0(grid,size,-origin).reshape(-1,3,order='F')
coords = damask.grid_filters.cell_coord0(grid,size,-origin).reshape(-1,3)
if cpus > 1:
pool = multiprocessing.Pool(processes = cpus)
result = pool.map_async(partial(findClosestSeed,seeds_p,weights_p), [coord for coord in coords])
pool.close()
pool.join()
closest_seed = np.array(result.get())
closest_seed = np.array(result.get()).reshape(-1,3)
else:
closest_seed= np.array([findClosestSeed(seeds_p,weights_p,coord) for coord in coords])
@ -52,7 +52,7 @@ def Laguerre_tessellation(grid, size, seeds, weights, origin = np.zeros(3), peri
def Voronoi_tessellation(grid, size, seeds, origin = np.zeros(3), periodic = True):
coords = damask.grid_filters.cell_coord0(grid,size,-origin).reshape(-1,3,order='F')
coords = damask.grid_filters.cell_coord0(grid,size,-origin).reshape(-1,3)
KDTree = spatial.cKDTree(seeds,boxsize=size) if periodic else spatial.cKDTree(seeds)
devNull,closest_seed = KDTree.query(coords)

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@ -54,7 +54,7 @@ for name in filenames:
np.in1d(microstructure,options.blacklist,invert=True) if options.blacklist else \
np.full(geom.grid.prod(),True,dtype=bool))
seeds = damask.grid_filters.cell_coord0(geom.grid,geom.size).reshape(-1,3)
seeds = damask.grid_filters.cell_coord0(geom.grid,geom.size).reshape(-1,3,order='F')
comments = geom.comments \
+ [scriptID + ' ' + ' '.join(sys.argv[1:]),

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@ -128,7 +128,7 @@ for name in filenames:
if not options.selective:
coords = damask.grid_filters.cell_coord0(grid,size).reshape(-1,3)
coords = damask.grid_filters.cell_coord0(grid,size).reshape(-1,3,order='F')
seeds = coords[np.random.choice(np.prod(grid), options.N, replace=False)] \
+ np.broadcast_to(size/grid,(options.N,3))*(np.random.rand(options.N,3)*.5-.25) # wobble without leaving grid
else:

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@ -322,11 +322,10 @@ class Geom:
if i != grid.prod():
raise TypeError('Invalid file: expected {} entries, found {}'.format(grid.prod(),i))
microstructure = microstructure.reshape(grid,order='F')
if not np.any(np.mod(microstructure.flatten(),1) != 0.0): # no float present
if not np.any(np.mod(microstructure,1) != 0.0): # no float present
microstructure = microstructure.astype('int')
return Geom(microstructure.reshape(grid),size,origin,homogenization,comments)
return Geom(microstructure.reshape(grid,order='F'),size,origin,homogenization,comments)
@staticmethod
@ -352,16 +351,15 @@ class Geom:
"""
if periodic:
weights_p = np.tile(weights,27).flatten(order='F') # Laguerre weights (1,2,3,1,2,3,...,1,2,3)
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]])))
coords = grid_filters.cell_coord0(grid*3,size*3,-size).reshape(-1,3,order='F')
coords = grid_filters.cell_coord0(grid*3,size*3,-size).reshape(-1,3)
else:
weights_p = weights.flatten()
weights_p = weights
seeds_p = seeds
coords = grid_filters.cell_coord0(grid,size).reshape(-1,3,order='F')
coords = grid_filters.cell_coord0(grid,size).reshape(-1,3)
pool = multiprocessing.Pool(processes = int(Environment().options['DAMASK_NUM_THREADS']))
result = pool.map_async(partial(Geom._find_closest_seed,seeds_p,weights_p), [coord for coord in coords])
@ -396,7 +394,7 @@ class Geom:
perform a periodic tessellation. Defaults to True.
"""
coords = grid_filters.cell_coord0(grid,size).reshape(-1,3,order='F')
coords = grid_filters.cell_coord0(grid,size).reshape(-1,3)
KDTree = spatial.cKDTree(seeds,boxsize=size) if periodic else spatial.cKDTree(seeds)
devNull,microstructure = KDTree.query(coords)

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@ -68,12 +68,12 @@ class Result:
self.con_physics = []
for c in self.constituents:
self.con_physics += f['/'.join([self.increments[0],'constituent',c])].keys()
self.con_physics = list(set(self.con_physics)) # make unique
self.con_physics = list(set(self.con_physics)) # make unique
self.mat_physics = []
for m in self.materialpoints:
self.mat_physics += f['/'.join([self.increments[0],'materialpoint',m])].keys()
self.mat_physics = list(set(self.mat_physics)) # make unique
self.mat_physics = list(set(self.mat_physics)) # make unique
self.selection = {'increments': self.increments,
'constituents': self.constituents,'materialpoints': self.materialpoints,
@ -86,13 +86,19 @@ class Result:
def __repr__(self):
"""Show selected data."""
all_selected_increments = self.selection['increments']
self.pick('increments',all_selected_increments[0:1])
first = self.list_data()
self.pick('increments',all_selected_increments[-1:])
last = self.list_data()
last = '' if len(all_selected_increments) < 2 else self.list_data()
self.pick('increments',all_selected_increments)
in_between = ''.join(['\n{}\n ...\n'.format(inc) for inc in all_selected_increments[1:-2]])
return util.srepr(first+ in_between + last)
in_between = '' if len(all_selected_increments) < 3 else \
''.join(['\n{}\n ...\n'.format(inc) for inc in all_selected_increments[1:-2]])
return util.srepr(first + in_between + last)
def _manage_selection(self,action,what,datasets):
@ -105,7 +111,7 @@ class Result:
select from 'set', 'add', and 'del'
what : str
attribute to change (must be from self.selection)
datasets : list of str or Boolean
datasets : list of str or bool
name of datasets as list, supports ? and * wildcards.
True is equivalent to [*], False is equivalent to []
@ -197,7 +203,7 @@ class Result:
----------
what : str
attribute to change (must be from self.selection)
datasets : list of str or Boolean
datasets : list of str or bool
name of datasets as list, supports ? and * wildcards.
True is equivalent to [*], False is equivalent to []
@ -213,7 +219,7 @@ class Result:
----------
what : str
attribute to change (must be from self.selection)
datasets : list of str or Boolean
datasets : list of str or bool
name of datasets as list, supports ? and * wildcards.
True is equivalent to [*], False is equivalent to []
@ -229,7 +235,7 @@ class Result:
----------
what : str
attribute to change (must be from self.selection)
datasets : list of str or Boolean
datasets : list of str or bool
name of datasets as list, supports ? and * wildcards.
True is equivalent to [*], False is equivalent to []
@ -256,10 +262,10 @@ class Result:
datasets : iterable or str
component : int
homogenization component to consider for constituent data
tagged : Boolean
tagged : bool
tag Table.column name with '#component'
defaults to False
split : Boolean
split : bool
split Table by increment and return dictionary of Tables
defaults to True
@ -320,7 +326,7 @@ class Result:
Parameters
----------
datasets : iterable or str or Boolean
datasets : iterable or str or bool
Examples
--------
@ -454,7 +460,7 @@ class Result:
def cell_coordinates(self):
"""Return initial coordinates of the cell centers."""
if self.structured:
return grid_filters.cell_coord0(self.grid,self.size,self.origin).reshape(-1,3)
return grid_filters.cell_coord0(self.grid,self.size,self.origin).reshape(-1,3,order='F')
else:
with h5py.File(self.fname,'r') as f:
return f['geometry/x_c'][()]
@ -1009,7 +1015,7 @@ class Result:
continue
lock.acquire()
with h5py.File(self.fname, 'a') as f:
try:
try: # ToDo: Replace if exists?
dataset = f[result[0]].create_dataset(result[1]['label'],data=result[1]['data'])
for l,v in result[1]['meta'].items():
dataset.attrs[l]=v.encode()

View File

@ -1,3 +1,17 @@
"""
Filters for operations on regular grids.
Notes
-----
The grids are defined as (x,y,z,...) where x is fastest and z is slowest.
This convention is consistent with the geom file format.
When converting to/from a plain list (e.g. storage in ASCII table),
the following operations are required for tensorial data:
D3 = D1.reshape(grid+(-1,),order='F').reshape(grid+(3,3))
D1 = D3.reshape(grid+(-1,)).reshape(-1,9,order='F')
"""
from scipy import spatial as _spatial
import numpy as _np
@ -7,8 +21,12 @@ def _ks(size,grid,first_order=False):
Parameters
----------
size : numpy.ndarray
size : numpy.ndarray of shape (3)
physical size of the periodic field.
grid : numpy.ndarray of shape (3)
number of grid points.
first_order : bool, optional
correction for first order derivatives, defaults to False.
"""
k_sk = _np.where(_np.arange(grid[0])>grid[0]//2,_np.arange(grid[0])-grid[0],_np.arange(grid[0]))/size[0]
@ -19,8 +37,7 @@ def _ks(size,grid,first_order=False):
k_si = _np.arange(grid[2]//2+1)/size[2]
kk, kj, ki = _np.meshgrid(k_sk,k_sj,k_si,indexing = 'ij')
return _np.concatenate((ki[:,:,:,None],kj[:,:,:,None],kk[:,:,:,None]),axis = 3)
return _np.stack(_np.meshgrid(k_sk,k_sj,k_si,indexing = 'ij'), axis=-1)
def curl(size,field):
@ -29,8 +46,10 @@ def curl(size,field):
Parameters
----------
size : numpy.ndarray
size : numpy.ndarray of shape (3)
physical size of the periodic field.
field : numpy.ndarray of shape (:,:,:,3) or (:,:,:,3,3)
periodic field of which the curl is calculated.
"""
n = _np.prod(field.shape[3:])
@ -41,8 +60,8 @@ def curl(size,field):
e[0, 2, 1] = e[2, 1, 0] = e[1, 0, 2] = -1.0
field_fourier = _np.fft.rfftn(field,axes=(0,1,2))
curl_ = (_np.einsum('slm,ijkl,ijkm ->ijks', e,k_s,field_fourier)*2.0j*_np.pi if n == 3 else # vector, 3 -> 3
_np.einsum('slm,ijkl,ijknm->ijksn',e,k_s,field_fourier)*2.0j*_np.pi) # tensor, 3x3 -> 3x3
curl_ = (_np.einsum('slm,ijkl,ijkm ->ijks', e,k_s,field_fourier)*2.0j*_np.pi if n == 3 else # vector, 3 -> 3
_np.einsum('slm,ijkl,ijknm->ijksn',e,k_s,field_fourier)*2.0j*_np.pi) # tensor, 3x3 -> 3x3
return _np.fft.irfftn(curl_,axes=(0,1,2),s=field.shape[:3])
@ -53,36 +72,40 @@ def divergence(size,field):
Parameters
----------
size : numpy.ndarray
size : numpy.ndarray of shape (3)
physical size of the periodic field.
field : numpy.ndarray of shape (:,:,:,3) or (:,:,:,3,3)
periodic field of which the divergence is calculated.
"""
n = _np.prod(field.shape[3:])
k_s = _ks(size,field.shape[:3],True)
field_fourier = _np.fft.rfftn(field,axes=(0,1,2))
div_ = (_np.einsum('ijkl,ijkl ->ijk', k_s,field_fourier)*2.0j*_np.pi if n == 3 else # vector, 3 -> 1
_np.einsum('ijkm,ijklm->ijkl',k_s,field_fourier)*2.0j*_np.pi) # tensor, 3x3 -> 3
div_ = (_np.einsum('ijkl,ijkl ->ijk', k_s,field_fourier)*2.0j*_np.pi if n == 3 else # vector, 3 -> 1
_np.einsum('ijkm,ijklm->ijkl',k_s,field_fourier)*2.0j*_np.pi) # tensor, 3x3 -> 3
return _np.fft.irfftn(div_,axes=(0,1,2),s=field.shape[:3])
def gradient(size,field):
"""
Calculate gradient of a vector or scalar field in Fourier space.
Calculate gradient of a scalar or vector field in Fourier space.
Parameters
----------
size : numpy.ndarray
size : numpy.ndarray of shape (3)
physical size of the periodic field.
field : numpy.ndarray of shape (:,:,:,1) or (:,:,:,3)
periodic field of which the gradient is calculated.
"""
n = _np.prod(field.shape[3:])
k_s = _ks(size,field.shape[:3],True)
field_fourier = _np.fft.rfftn(field,axes=(0,1,2))
grad_ = (_np.einsum('ijkl,ijkm->ijkm', field_fourier,k_s)*2.0j*_np.pi if n == 1 else # scalar, 1 -> 3
_np.einsum('ijkl,ijkm->ijklm',field_fourier,k_s)*2.0j*_np.pi) # vector, 3 -> 3x3
grad_ = (_np.einsum('ijkl,ijkm->ijkm', field_fourier,k_s)*2.0j*_np.pi if n == 1 else # scalar, 1 -> 3
_np.einsum('ijkl,ijkm->ijklm',field_fourier,k_s)*2.0j*_np.pi) # vector, 3 -> 3x3
return _np.fft.irfftn(grad_,axes=(0,1,2),s=field.shape[:3])
@ -93,9 +116,9 @@ def cell_coord0(grid,size,origin=_np.zeros(3)):
Parameters
----------
grid : numpy.ndarray
grid : numpy.ndarray of shape (3)
number of grid points.
size : numpy.ndarray
size : numpy.ndarray of shape (3)
physical size of the periodic field.
origin : numpy.ndarray, optional
physical origin of the periodic field. Defaults to [0.0,0.0,0.0].
@ -103,7 +126,11 @@ def cell_coord0(grid,size,origin=_np.zeros(3)):
"""
start = origin + size/grid*.5
end = origin + size - size/grid*.5
return _np.mgrid[start[0]:end[0]:grid[0]*1j,start[1]:end[1]:grid[1]*1j,start[2]:end[2]:grid[2]*1j].T
return _np.stack(_np.meshgrid(_np.linspace(start[0],end[0],grid[0]),
_np.linspace(start[1],end[1],grid[1]),
_np.linspace(start[2],end[2],grid[2]),indexing = 'ij'),
axis = -1)
def cell_displacement_fluct(size,F):
@ -112,7 +139,7 @@ def cell_displacement_fluct(size,F):
Parameters
----------
size : numpy.ndarray
size : numpy.ndarray of shape (3)
physical size of the periodic field.
F : numpy.ndarray
deformation gradient field.
@ -139,14 +166,14 @@ def cell_displacement_avg(size,F):
Parameters
----------
size : numpy.ndarray
size : numpy.ndarray of shape (3)
physical size of the periodic field.
F : numpy.ndarray
deformation gradient field.
"""
F_avg = _np.average(F,axis=(0,1,2))
return _np.einsum('ml,ijkl->ijkm',F_avg-_np.eye(3),cell_coord0(F.shape[:3][::-1],size))
return _np.einsum('ml,ijkl->ijkm',F_avg - _np.eye(3),cell_coord0(F.shape[:3],size))
def cell_displacement(size,F):
@ -155,7 +182,7 @@ def cell_displacement(size,F):
Parameters
----------
size : numpy.ndarray
size : numpy.ndarray of shape (3)
physical size of the periodic field.
F : numpy.ndarray
deformation gradient field.
@ -170,25 +197,25 @@ def cell_coord(size,F,origin=_np.zeros(3)):
Parameters
----------
size : numpy.ndarray
size : numpy.ndarray of shape (3)
physical size of the periodic field.
F : numpy.ndarray
deformation gradient field.
origin : numpy.ndarray, optional
origin : numpy.ndarray of shape (3), optional
physical origin of the periodic field. Defaults to [0.0,0.0,0.0].
"""
return cell_coord0(F.shape[:3][::-1],size,origin) + cell_displacement(size,F)
return cell_coord0(F.shape[:3],size,origin) + cell_displacement(size,F)
def cell_coord0_gridSizeOrigin(coord0,ordered=True):
"""
Return grid 'DNA', i.e. grid, size, and origin from array of cell positions.
Return grid 'DNA', i.e. grid, size, and origin from 1D array of cell positions.
Parameters
----------
coord0 : numpy.ndarray
array of undeformed cell coordinates.
coord0 : numpy.ndarray of shape (:,3)
undeformed cell coordinates.
ordered : bool, optional
expect coord0 data to be ordered (x fast, z slow).
@ -211,13 +238,13 @@ def cell_coord0_gridSizeOrigin(coord0,ordered=True):
start = origin + delta*.5
end = origin - delta*.5 + size
if not _np.allclose(coords[0],_np.linspace(start[0],end[0],grid[0])) and \
_np.allclose(coords[1],_np.linspace(start[1],end[1],grid[1])) and \
_np.allclose(coords[2],_np.linspace(start[2],end[2],grid[2])):
if not (_np.allclose(coords[0],_np.linspace(start[0],end[0],grid[0])) and \
_np.allclose(coords[1],_np.linspace(start[1],end[1],grid[1])) and \
_np.allclose(coords[2],_np.linspace(start[2],end[2],grid[2]))):
raise ValueError('Regular grid spacing violated.')
if ordered and not _np.allclose(coord0.reshape(tuple(grid[::-1])+(3,)),cell_coord0(grid,size,origin)):
raise ValueError('I_nput data is not a regular grid.')
if ordered and not _np.allclose(coord0.reshape(tuple(grid)+(3,),order='F'),cell_coord0(grid,size,origin)):
raise ValueError('Input data is not ordered (x fast, z slow).')
return (grid,size,origin)
@ -241,17 +268,18 @@ def node_coord0(grid,size,origin=_np.zeros(3)):
Parameters
----------
grid : numpy.ndarray
grid : numpy.ndarray of shape (3)
number of grid points.
size : numpy.ndarray
size : numpy.ndarray of shape (3)
physical size of the periodic field.
origin : numpy.ndarray, optional
origin : numpy.ndarray of shape (3), optional
physical origin of the periodic field. Defaults to [0.0,0.0,0.0].
"""
return _np.mgrid[origin[0]:size[0]+origin[0]:(grid[0]+1)*1j,
origin[1]:size[1]+origin[1]:(grid[1]+1)*1j,
origin[2]:size[2]+origin[2]:(grid[2]+1)*1j].T
return _np.stack(_np.meshgrid(_np.linspace(origin[0],size[0]+origin[0],grid[0]+1),
_np.linspace(origin[1],size[1]+origin[1],grid[1]+1),
_np.linspace(origin[2],size[2]+origin[2],grid[2]+1),indexing = 'ij'),
axis = -1)
def node_displacement_fluct(size,F):
@ -260,7 +288,7 @@ def node_displacement_fluct(size,F):
Parameters
----------
size : numpy.ndarray
size : numpy.ndarray of shape (3)
physical size of the periodic field.
F : numpy.ndarray
deformation gradient field.
@ -275,14 +303,14 @@ def node_displacement_avg(size,F):
Parameters
----------
size : numpy.ndarray
size : numpy.ndarray of shape (3)
physical size of the periodic field.
F : numpy.ndarray
deformation gradient field.
"""
F_avg = _np.average(F,axis=(0,1,2))
return _np.einsum('ml,ijkl->ijkm',F_avg-_np.eye(3),node_coord0(F.shape[:3][::-1],size))
return _np.einsum('ml,ijkl->ijkm',F_avg - _np.eye(3),node_coord0(F.shape[:3],size))
def node_displacement(size,F):
@ -291,7 +319,7 @@ def node_displacement(size,F):
Parameters
----------
size : numpy.ndarray
size : numpy.ndarray of shape (3)
physical size of the periodic field.
F : numpy.ndarray
deformation gradient field.
@ -306,15 +334,15 @@ def node_coord(size,F,origin=_np.zeros(3)):
Parameters
----------
size : numpy.ndarray
size : numpy.ndarray of shape (3)
physical size of the periodic field.
F : numpy.ndarray
deformation gradient field.
origin : numpy.ndarray, optional
origin : numpy.ndarray of shape (3), optional
physical origin of the periodic field. Defaults to [0.0,0.0,0.0].
"""
return node_coord0(F.shape[:3][::-1],size,origin) + node_displacement(size,F)
return node_coord0(F.shape[:3],size,origin) + node_displacement(size,F)
def cell_2_node(cell_data):
@ -335,14 +363,14 @@ def node_2_cell(node_data):
return c[:-1,:-1,:-1]
def node_coord0_gridSizeOrigin(coord0,ordered=False):
def node_coord0_gridSizeOrigin(coord0,ordered=True):
"""
Return grid 'DNA', i.e. grid, size, and origin from array of nodal positions.
Return grid 'DNA', i.e. grid, size, and origin from 1D array of nodal positions.
Parameters
----------
coord0 : numpy.ndarray
array of undeformed nodal coordinates.
coord0 : numpy.ndarray of shape (:,3)
undeformed nodal coordinates.
ordered : bool, optional
expect coord0 data to be ordered (x fast, z slow).
@ -357,13 +385,13 @@ def node_coord0_gridSizeOrigin(coord0,ordered=False):
if (grid+1).prod() != len(coord0):
raise ValueError('Data count {} does not match grid {}.'.format(len(coord0),grid))
if not _np.allclose(coords[0],_np.linspace(mincorner[0],maxcorner[0],grid[0]+1)) and \
_np.allclose(coords[1],_np.linspace(mincorner[1],maxcorner[1],grid[1]+1)) and \
_np.allclose(coords[2],_np.linspace(mincorner[2],maxcorner[2],grid[2]+1)):
if not (_np.allclose(coords[0],_np.linspace(mincorner[0],maxcorner[0],grid[0]+1)) and \
_np.allclose(coords[1],_np.linspace(mincorner[1],maxcorner[1],grid[1]+1)) and \
_np.allclose(coords[2],_np.linspace(mincorner[2],maxcorner[2],grid[2]+1))):
raise ValueError('Regular grid spacing violated.')
if ordered and not _np.allclose(coord0.reshape(tuple((grid+1)[::-1])+(3,)),node_coord0(grid,size,origin)):
raise ValueError('I_nput data is not a regular grid.')
if ordered and not _np.allclose(coord0.reshape(tuple(grid+1)+(3,),order='F'),node_coord0(grid,size,origin)):
raise ValueError('Input data is not ordered (x fast, z slow).')
return (grid,size,origin)
@ -374,15 +402,15 @@ def regrid(size,F,new_grid):
Parameters
----------
size : numpy.ndarray
size : numpy.ndarray of shape (3)
physical size
F : numpy.ndarray
F : numpy.ndarray of shape (:,:,:,3,3)
deformation gradient field
new_grid : numpy.ndarray
new_grid : numpy.ndarray of shape (3)
new grid for undeformed coordinates
"""
c = cell_coord0(F.shape[:3][::-1],size) \
c = cell_coord0(F.shape[:3],size) \
+ cell_displacement_avg(size,F) \
+ cell_displacement_fluct(size,F)

View File

@ -24,6 +24,10 @@ def reference_dir(reference_dir_base):
class TestResult:
def test_self_report(self,default):
print(default)
def test_time_increments(self,default):
shape = default.read_dataset(default.get_dataset_location('F'),0).shape
default.set_by_time(0.0,20.0)

View File

@ -9,13 +9,13 @@ class TestGridFilters:
size = np.random.random(3)
grid = np.random.randint(8,32,(3))
coord = grid_filters.cell_coord0(grid,size)
assert np.allclose(coord[0,0,0],size/grid*.5) and coord.shape == tuple(grid[::-1]) + (3,)
assert np.allclose(coord[0,0,0],size/grid*.5) and coord.shape == tuple(grid) + (3,)
def test_node_coord0(self):
size = np.random.random(3)
grid = np.random.randint(8,32,(3))
coord = grid_filters.node_coord0(grid,size)
assert np.allclose(coord[-1,-1,-1],size) and coord.shape == tuple(grid[::-1]+1) + (3,)
assert np.allclose(coord[-1,-1,-1],size) and coord.shape == tuple(grid+1) + (3,)
def test_coord0(self):
size = np.random.random(3)
@ -31,7 +31,7 @@ class TestGridFilters:
size = np.random.random(3)
origin = np.random.random(3)
coord0 = eval('grid_filters.{}_coord0(grid,size,origin)'.format(mode)) # noqa
_grid,_size,_origin = eval('grid_filters.{}_coord0_gridSizeOrigin(coord0.reshape(-1,3))'.format(mode))
_grid,_size,_origin = eval('grid_filters.{}_coord0_gridSizeOrigin(coord0.reshape(-1,3,order="F"))'.format(mode))
assert np.allclose(grid,_grid) and np.allclose(size,_size) and np.allclose(origin,_origin)
def test_displacement_fluct_equivalence(self):
@ -57,9 +57,9 @@ class TestGridFilters:
shifted = eval('grid_filters.{}_coord0(grid,size,origin)'.format(mode))
unshifted = eval('grid_filters.{}_coord0(grid,size)'.format(mode))
if mode == 'cell':
assert np.allclose(shifted,unshifted+np.broadcast_to(origin,tuple(grid[::-1]) +(3,)))
assert np.allclose(shifted,unshifted+np.broadcast_to(origin,tuple(grid) +(3,)))
elif mode == 'node':
assert np.allclose(shifted,unshifted+np.broadcast_to(origin,tuple(grid[::-1]+1)+(3,)))
assert np.allclose(shifted,unshifted+np.broadcast_to(origin,tuple(grid+1)+(3,)))
@pytest.mark.parametrize('function',[grid_filters.cell_displacement_avg,
grid_filters.node_displacement_avg])
@ -80,8 +80,43 @@ class TestGridFilters:
F = np.broadcast_to(np.random.random((3,3)), tuple(grid)+(3,3))
assert np.allclose(function(size,F),0.0)
@pytest.mark.parametrize('function',[grid_filters.coord0_check,
grid_filters.node_coord0_gridSizeOrigin,
grid_filters.cell_coord0_gridSizeOrigin])
def test_invalid_coordinates(self,function):
invalid_coordinates = np.random.random((np.random.randint(12,52),3))
with pytest.raises(ValueError):
function(invalid_coordinates)
@pytest.mark.parametrize('function',[grid_filters.node_coord0_gridSizeOrigin,
grid_filters.cell_coord0_gridSizeOrigin])
def test_uneven_spaced_coordinates(self,function):
start = np.random.random(3)
end = np.random.random(3)*10. + start
grid = np.random.randint(8,32,(3))
uneven = np.stack(np.meshgrid(np.logspace(start[0],end[0],grid[0]),
np.logspace(start[1],end[1],grid[1]),
np.logspace(start[2],end[2],grid[2]),indexing = 'ij'),
axis = -1).reshape((grid.prod(),3),order='F')
with pytest.raises(ValueError):
function(uneven)
@pytest.mark.parametrize('mode',[True,False])
@pytest.mark.parametrize('function',[grid_filters.node_coord0_gridSizeOrigin,
grid_filters.cell_coord0_gridSizeOrigin])
def test_unordered_coordinates(self,function,mode):
origin = np.random.random(3)
size = np.random.random(3)*10.+origin
grid = np.random.randint(8,32,(3))
unordered = grid_filters.node_coord0(grid,size,origin).reshape(-1,3)
if mode:
with pytest.raises(ValueError):
function(unordered,mode)
else:
function(unordered,mode)
def test_regrid(self):
size = np.random.random(3)
grid = np.random.randint(8,32,(3))
F = np.broadcast_to(np.eye(3), tuple(grid[::-1])+(3,3))
F = np.broadcast_to(np.eye(3), tuple(grid)+(3,3))
assert all(grid_filters.regrid(size,F,grid) == np.arange(grid.prod()))

View File

@ -184,8 +184,6 @@ subroutine materialpoint_stressAndItsTangent(updateJaco,dt)
e, & !< element number
mySource, &
myNgrains
real(pReal), dimension(3,3) :: &
subF
real(pReal), dimension(discretization_nIP,discretization_nElem) :: &
subFrac, &
subStep
@ -376,16 +374,15 @@ subroutine materialpoint_stressAndItsTangent(updateJaco,dt)
!--------------------------------------------------------------------------------------------------
! deformation partitioning
! based on materialpoint_subF0,.._subF,crystallite_partionedF0, and homogenization_state,
! results in crystallite_partionedF
!$OMP PARALLEL DO PRIVATE(myNgrains,subF)
!$OMP PARALLEL DO PRIVATE(myNgrains)
elementLooping2: do e = FEsolving_execElem(1),FEsolving_execElem(2)
myNgrains = homogenization_Ngrains(material_homogenizationAt(e))
IpLooping2: do i = FEsolving_execIP(1),FEsolving_execIP(2)
if(requested(i,e) .and. .not. doneAndHappy(1,i,e)) then ! requested but not yet done
subF = materialpoint_F0(1:3,1:3,i,e) &
+ (materialpoint_F(1:3,1:3,i,e)-materialpoint_F0(1:3,1:3,i,e))*(subStep(i,e)+subFrac(i,e))
call partitionDeformation(subF,i,e) ! partition deformation onto constituents
call partitionDeformation(materialpoint_F0(1:3,1:3,i,e) &
+ (materialpoint_F(1:3,1:3,i,e)-materialpoint_F0(1:3,1:3,i,e))&
*(subStep(i,e)+subFrac(i,e)), &
i,e)
crystallite_dt(1:myNgrains,i,e) = dt*subStep(i,e) ! propagate materialpoint dt to grains
crystallite_requested(1:myNgrains,i,e) = .true. ! request calculation for constituents
else
@ -397,23 +394,22 @@ subroutine materialpoint_stressAndItsTangent(updateJaco,dt)
!--------------------------------------------------------------------------------------------------
! crystallite integration
! based on crystallite_partionedF0,.._partionedF
! incrementing by crystallite_dt
converged = crystallite_stress() !ToDo: MD not sure if that is the best logic
!--------------------------------------------------------------------------------------------------
! state update
!$OMP PARALLEL DO PRIVATE(subF)
!$OMP PARALLEL DO
elementLooping3: do e = FEsolving_execElem(1),FEsolving_execElem(2)
IpLooping3: do i = FEsolving_execIP(1),FEsolving_execIP(2)
if (requested(i,e) .and. .not. doneAndHappy(1,i,e)) then
if (.not. converged(i,e)) then
doneAndHappy(1:2,i,e) = [.true.,.false.]
else
subF = materialpoint_F0(1:3,1:3,i,e) &
+ (materialpoint_F(1:3,1:3,i,e)-materialpoint_F0(1:3,1:3,i,e))*(subStep(i,e)+subFrac(i,e))
doneAndHappy(1:2,i,e) = updateState(dt*subStep(i,e),subF,i,e)
doneAndHappy(1:2,i,e) = updateState(dt*subStep(i,e), &
materialpoint_F0(1:3,1:3,i,e) &
+ (materialpoint_F(1:3,1:3,i,e)-materialpoint_F0(1:3,1:3,i,e)) &
*(subStep(i,e)+subFrac(i,e)), &
i,e)
converged(i,e) = all(doneAndHappy(1:2,i,e)) ! converged if done and happy
endif
endif

View File

@ -118,7 +118,7 @@ end subroutine quaternions_init
!---------------------------------------------------------------------------------------------------
!> construct a quaternion from a 4-vector
!> @brief construct a quaternion from a 4-vector
!---------------------------------------------------------------------------------------------------
type(quaternion) pure function init__(array)
@ -133,7 +133,7 @@ end function init__
!---------------------------------------------------------------------------------------------------
!> assign a quaternion
!> @brief assign a quaternion
!---------------------------------------------------------------------------------------------------
elemental pure subroutine assign_quat__(self,other)
@ -146,7 +146,7 @@ end subroutine assign_quat__
!---------------------------------------------------------------------------------------------------
!> assign a 4-vector
!> @brief assign a 4-vector
!---------------------------------------------------------------------------------------------------
pure subroutine assign_vec__(self,other)
@ -162,7 +162,7 @@ end subroutine assign_vec__
!---------------------------------------------------------------------------------------------------
!> add a quaternion
!> @brief add a quaternion
!---------------------------------------------------------------------------------------------------
type(quaternion) elemental pure function add__(self,other)
@ -175,7 +175,7 @@ end function add__
!---------------------------------------------------------------------------------------------------
!> return (unary positive operator)
!> @brief return (unary positive operator)
!---------------------------------------------------------------------------------------------------
type(quaternion) elemental pure function pos__(self)
@ -187,7 +187,7 @@ end function pos__
!---------------------------------------------------------------------------------------------------
!> subtract a quaternion
!> @brief subtract a quaternion
!---------------------------------------------------------------------------------------------------
type(quaternion) elemental pure function sub__(self,other)
@ -200,7 +200,7 @@ end function sub__
!---------------------------------------------------------------------------------------------------
!> negate (unary negative operator)
!> @brief negate (unary negative operator)
!---------------------------------------------------------------------------------------------------
type(quaternion) elemental pure function neg__(self)
@ -212,7 +212,7 @@ end function neg__
!---------------------------------------------------------------------------------------------------
!> multiply with a quaternion
!> @brief multiply with a quaternion
!---------------------------------------------------------------------------------------------------
type(quaternion) elemental pure function mul_quat__(self,other)
@ -227,7 +227,7 @@ end function mul_quat__
!---------------------------------------------------------------------------------------------------
!> multiply with a scalar
!> @brief multiply with a scalar
!---------------------------------------------------------------------------------------------------
type(quaternion) elemental pure function mul_scal__(self,scal)
@ -240,7 +240,7 @@ end function mul_scal__
!---------------------------------------------------------------------------------------------------
!> divide by a quaternion
!> @brief divide by a quaternion
!---------------------------------------------------------------------------------------------------
type(quaternion) elemental pure function div_quat__(self,other)
@ -252,7 +252,7 @@ end function div_quat__
!---------------------------------------------------------------------------------------------------
!> divide by a scalar
!> @brief divide by a scalar
!---------------------------------------------------------------------------------------------------
type(quaternion) elemental pure function div_scal__(self,scal)
@ -265,7 +265,7 @@ end function div_scal__
!---------------------------------------------------------------------------------------------------
!> test equality
!> @brief test equality
!---------------------------------------------------------------------------------------------------
logical elemental pure function eq__(self,other)
@ -278,7 +278,7 @@ end function eq__
!---------------------------------------------------------------------------------------------------
!> test inequality
!> @brief test inequality
!---------------------------------------------------------------------------------------------------
logical elemental pure function neq__(self,other)
@ -290,7 +290,7 @@ end function neq__
!---------------------------------------------------------------------------------------------------
!> raise to the power of a quaternion
!> @brief raise to the power of a quaternion
!---------------------------------------------------------------------------------------------------
type(quaternion) elemental pure function pow_quat__(self,expon)
@ -303,7 +303,7 @@ end function pow_quat__
!---------------------------------------------------------------------------------------------------
!> raise to the power of a scalar
!> @brief raise to the power of a scalar
!---------------------------------------------------------------------------------------------------
type(quaternion) elemental pure function pow_scal__(self,expon)
@ -316,7 +316,7 @@ end function pow_scal__
!---------------------------------------------------------------------------------------------------
!> take exponential
!> @brief take exponential
!---------------------------------------------------------------------------------------------------
type(quaternion) elemental pure function exp__(a)
@ -336,7 +336,7 @@ end function exp__
!---------------------------------------------------------------------------------------------------
!> take logarithm
!> @brief take logarithm
!---------------------------------------------------------------------------------------------------
type(quaternion) elemental pure function log__(a)
@ -356,7 +356,7 @@ end function log__
!---------------------------------------------------------------------------------------------------
!> return norm
!> @brief return norm
!---------------------------------------------------------------------------------------------------
real(pReal) elemental pure function abs__(self)
@ -368,7 +368,7 @@ end function abs__
!---------------------------------------------------------------------------------------------------
!> calculate dot product
!> @brief calculate dot product
!---------------------------------------------------------------------------------------------------
real(pReal) elemental pure function dot_product__(a,b)
@ -380,7 +380,7 @@ end function dot_product__
!---------------------------------------------------------------------------------------------------
!> take conjugate complex
!> @brief take conjugate complex
!---------------------------------------------------------------------------------------------------
type(quaternion) elemental pure function conjg__(self)
@ -392,7 +392,7 @@ end function conjg__
!---------------------------------------------------------------------------------------------------
!> homomorph
!> @brief homomorph
!---------------------------------------------------------------------------------------------------
type(quaternion) elemental pure function homomorphed(self)
@ -404,7 +404,7 @@ end function homomorphed
!---------------------------------------------------------------------------------------------------
!> return as plain array
!> @brief return as plain array
!---------------------------------------------------------------------------------------------------
pure function asArray(self)
@ -417,7 +417,7 @@ end function asArray
!---------------------------------------------------------------------------------------------------
!> real part (scalar)
!> @brief real part (scalar)
!---------------------------------------------------------------------------------------------------
pure function real__(self)
@ -430,7 +430,7 @@ end function real__
!---------------------------------------------------------------------------------------------------
!> imaginary part (3-vector)
!> @brief imaginary part (3-vector)
!---------------------------------------------------------------------------------------------------
pure function aimag__(self)
@ -443,7 +443,7 @@ end function aimag__
!---------------------------------------------------------------------------------------------------
!> inverse
!> @brief inverse
!---------------------------------------------------------------------------------------------------
type(quaternion) elemental pure function inverse(self)