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DAMASK_EICMD
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centralized facilities for differential operations 

note the need to reverse the grid shape in data from the ASCII table. If x is fastest,
z is slowest we require x to be the rightmost index
This commit is contained in:
Martin Diehl 2019-11-28 15:46:22 +01:00
parent 80b50f460e
commit 3e65d44e07
4 changed files with 74 additions and 402 deletions
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138
processing/post/addCurl.py
View File

@ -2,6 +2,7 @@
import os
import sys
from io import StringIO
from optparse import OptionParser
import numpy as np
@ -12,47 +13,6 @@ import damask
scriptName = os.path.splitext(os.path.basename(__file__))[0]
scriptID = ' '.join([scriptName,damask.version])
def merge_dicts(*dict_args):
"""Given any number of dicts, shallow copy and merge into a new dict, with precedence going to key value pairs in latter dicts."""
result = {}
for dictionary in dict_args:
result.update(dictionary)
return result
def curlFFT(geomdim,field):
"""Calculate curl of a vector or tensor field by transforming into Fourier space."""
shapeFFT = np.array(np.shape(field))[0:3]
grid = np.array(np.shape(field)[2::-1])
N = grid.prod() # field size
n = np.array(np.shape(field)[3:]).prod() # data size
field_fourier = np.fft.rfftn(field,axes=(0,1,2),s=shapeFFT)
# differentiation in Fourier space
TWOPIIMG = 2.0j*np.pi
einsums = {
3:'slm,ijkl,ijkm->ijks', # vector, 3 -> 3
9:'slm,ijkl,ijknm->ijksn', # tensor, 3x3 -> 3x3
}
k_sk = np.where(np.arange(grid[2])>grid[2]//2,np.arange(grid[2])-grid[2],np.arange(grid[2]))/geomdim[0]
if grid[2]%2 == 0: k_sk[grid[2]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011)
k_sj = np.where(np.arange(grid[1])>grid[1]//2,np.arange(grid[1])-grid[1],np.arange(grid[1]))/geomdim[1]
if grid[1]%2 == 0: k_sj[grid[1]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011)
k_si = np.arange(grid[0]//2+1)/geomdim[2]
kk, kj, ki = np.meshgrid(k_sk,k_sj,k_si,indexing = 'ij')
k_s = np.concatenate((ki[:,:,:,None],kj[:,:,:,None],kk[:,:,:,None]),axis = 3).astype('c16')
e = np.zeros((3, 3, 3))
e[0, 1, 2] = e[1, 2, 0] = e[2, 0, 1] = 1.0 # Levi-Civita symbols
e[0, 2, 1] = e[2, 1, 0] = e[1, 0, 2] = -1.0
curl_fourier = np.einsum(einsums[n],e,k_s,field_fourier)*TWOPIIMG
return np.fft.irfftn(curl_fourier,axes=(0,1,2),s=shapeFFT).reshape([N,n])
# --------------------------------------------------------------------
# MAIN
@ -60,8 +20,7 @@ def curlFFT(geomdim,field):
parser = OptionParser(option_class=damask.extendableOption, usage='%prog options [ASCIItable(s)]', description = """
Add column(s) containing curl of requested column(s).
Operates on periodic ordered three-dimensional data sets
of vector and tensor fields.
Operates on periodic ordered three-dimensional data sets of vector and tensor fields.
""", version = scriptID)
parser.add_option('-p','--pos','--periodiccellcenter',
@ -69,93 +28,30 @@ parser.add_option('-p','--pos','--periodiccellcenter',
type = 'string', metavar = 'string',
help = 'label of coordinates [%default]')
parser.add_option('-l','--label',
dest = 'data',
dest = 'labels',
action = 'extend', metavar = '<string LIST>',
help = 'label(s) of field values')
parser.set_defaults(pos = 'pos',
)
(options,filenames) = parser.parse_args()
if options.data is None: parser.error('no data column specified.')
# --- define possible data types -------------------------------------------------------------------
datatypes = {
3: {'name': 'vector',
'shape': [3],
},
9: {'name': 'tensor',
'shape': [3,3],
},
}
# --- loop over input files ------------------------------------------------------------------------
if filenames == []: filenames = [None]
if options.labels is None: parser.error('no data column specified.')
for name in filenames:
try: table = damask.ASCIItable(name = name,buffered = False)
except: continue
damask.util.report(scriptName,name)
damask.util.report(scriptName,name)
# --- interpret header ----------------------------------------------------------------------------
table = damask.Table.from_ASCII(StringIO(''.join(sys.stdin.read())) if name is None else name)
grid,size = damask.util.coordGridAndSize(table.get_array(options.pos))
table.head_read()
remarks = []
errors = []
active = []
coordDim = table.label_dimension(options.pos)
if coordDim != 3:
errors.append('coordinates "{}" must be three-dimensional.'.format(options.pos))
else: coordCol = table.label_index(options.pos)
for me in options.data:
dim = table.label_dimension(me)
if dim in datatypes:
active.append(merge_dicts({'label':me},datatypes[dim]))
remarks.append('differentiating {} "{}"...'.format(datatypes[dim]['name'],me))
else:
remarks.append('skipping "{}" of dimension {}...'.format(me,dim) if dim != -1 else \
'"{}" not found...'.format(me) )
if remarks != []: damask.util.croak(remarks)
if errors != []:
damask.util.croak(errors)
table.close(dismiss = True)
continue
# ------------------------------------------ assemble header --------------------------------------
table.info_append(scriptID + '\t' + ' '.join(sys.argv[1:]))
for data in active:
table.labels_append(['{}_curlFFT({})'.format(i+1,data['label'])
for i in range(np.prod(np.array(data['shape'])))]) # extend ASCII header with new labels
table.head_write()
# --------------- figure out size and grid ---------------------------------------------------------
table.data_readArray()
grid,size = damask.util.coordGridAndSize(table.data[:,table.label_indexrange(options.pos)])
# ------------------------------------------ process value field -----------------------------------
stack = [table.data]
for data in active:
# we need to reverse order here, because x is fastest,ie rightmost, but leftmost in our x,y,z notation
stack.append(curlFFT(size[::-1],
table.data[:,table.label_indexrange(data['label'])].
reshape(grid[::-1].tolist()+data['shape'])))
# ------------------------------------------ output result -----------------------------------------
if len(stack) > 1: table.data = np.hstack(tuple(stack))
table.data_writeArray('%.12g')
# ------------------------------------------ output finalization -----------------------------------
table.close() # close input ASCII table (works for stdin)
for label in options.labels:
field = table.get_array(label)
shape = (3,) if np.prod(field.shape)//np.prod(grid) == 3 else (3,3) # vector or tensor
field = table.get_array(label).reshape(np.append(grid[::-1],shape))
table.add_array('curlFFT({})'.format(label),
damask.grid_filters.curl(size[::-1],field).reshape((-1,np.prod(shape))),
scriptID+' '+' '.join(sys.argv[1:]))
table.to_ASCII(sys.stdout if name is None else name)

140
processing/post/addDivergence.py
View File

@ -2,6 +2,7 @@
import os
import sys
from io import StringIO
from optparse import OptionParser
import numpy as np
@ -12,52 +13,14 @@ import damask
scriptName = os.path.splitext(os.path.basename(__file__))[0]
scriptID = ' '.join([scriptName,damask.version])
def merge_dicts(*dict_args):
"""Given any number of dicts, shallow copy and merge into a new dict, with precedence going to key value pairs in latter dicts."""
result = {}
for dictionary in dict_args:
result.update(dictionary)
return result
def divFFT(geomdim,field):
"""Calculate divergence of a vector or tensor field by transforming into Fourier space."""
shapeFFT = np.array(np.shape(field))[0:3]
grid = np.array(np.shape(field)[2::-1])
N = grid.prod() # field size
n = np.array(np.shape(field)[3:]).prod() # data size
field_fourier = np.fft.rfftn(field,axes=(0,1,2),s=shapeFFT)
# differentiation in Fourier space
TWOPIIMG = 2.0j*np.pi
einsums = {
3:'ijkl,ijkl->ijk', # vector, 3 -> 1
9:'ijkm,ijklm->ijkl', # tensor, 3x3 -> 3
}
k_sk = np.where(np.arange(grid[2])>grid[2]//2,np.arange(grid[2])-grid[2],np.arange(grid[2]))/geomdim[0]
if grid[2]%2 == 0: k_sk[grid[2]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011)
k_sj = np.where(np.arange(grid[1])>grid[1]//2,np.arange(grid[1])-grid[1],np.arange(grid[1]))/geomdim[1]
if grid[1]%2 == 0: k_sj[grid[1]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011)
k_si = np.arange(grid[0]//2+1)/geomdim[2]
kk, kj, ki = np.meshgrid(k_sk,k_sj,k_si,indexing = 'ij')
k_s = np.concatenate((ki[:,:,:,None],kj[:,:,:,None],kk[:,:,:,None]),axis = 3).astype('c16')
div_fourier = np.einsum(einsums[n],k_s,field_fourier)*TWOPIIMG
return np.fft.irfftn(div_fourier,axes=(0,1,2),s=shapeFFT).reshape([N,n//3])
# --------------------------------------------------------------------
# MAIN
# --------------------------------------------------------------------
parser = OptionParser(option_class=damask.extendableOption, usage='%prog option(s) [ASCIItable(s)]', description = """
Add column(s) containing curl of requested column(s).
Operates on periodic ordered three-dimensional data sets
of vector and tensor fields.
parser = OptionParser(option_class=damask.extendableOption, usage='%prog options [ASCIItable(s)]', description = """
Add column(s) containing divergence of requested column(s).
Operates on periodic ordered three-dimensional data sets of vector and tensor fields.
""", version = scriptID)
parser.add_option('-p','--pos','--periodiccellcenter',
@ -65,95 +28,30 @@ parser.add_option('-p','--pos','--periodiccellcenter',
type = 'string', metavar = 'string',
help = 'label of coordinates [%default]')
parser.add_option('-l','--label',
dest = 'data',
dest = 'labels',
action = 'extend', metavar = '<string LIST>',
help = 'label(s) of field values')
parser.set_defaults(pos = 'pos',
)
(options,filenames) = parser.parse_args()
if options.data is None: parser.error('no data column specified.')
# --- define possible data types -------------------------------------------------------------------
datatypes = {
3: {'name': 'vector',
'shape': [3],
},
9: {'name': 'tensor',
'shape': [3,3],
},
}
# --- loop over input files ------------------------------------------------------------------------
if filenames == []: filenames = [None]
if options.labels is None: parser.error('no data column specified.')
for name in filenames:
try: table = damask.ASCIItable(name = name,buffered = False)
except: continue
damask.util.report(scriptName,name)
damask.util.report(scriptName,name)
# --- interpret header ----------------------------------------------------------------------------
table = damask.Table.from_ASCII(StringIO(''.join(sys.stdin.read())) if name is None else name)
grid,size = damask.util.coordGridAndSize(table.get_array(options.pos))
table.head_read()
remarks = []
errors = []
active = []
coordDim = table.label_dimension(options.pos)
if coordDim != 3:
errors.append('coordinates "{}" must be three-dimensional.'.format(options.pos))
else: coordCol = table.label_index(options.pos)
for me in options.data:
dim = table.label_dimension(me)
if dim in datatypes:
active.append(merge_dicts({'label':me},datatypes[dim]))
remarks.append('differentiating {} "{}"...'.format(datatypes[dim]['name'],me))
else:
remarks.append('skipping "{}" of dimension {}...'.format(me,dim) if dim != -1 else \
'"{}" not found...'.format(me) )
if remarks != []: damask.util.croak(remarks)
if errors != []:
damask.util.croak(errors)
table.close(dismiss = True)
continue
# ------------------------------------------ assemble header --------------------------------------
table.info_append(scriptID + '\t' + ' '.join(sys.argv[1:]))
for data in active:
table.labels_append(['divFFT({})'.format(data['label']) if data['shape'] == [3] \
else '{}_divFFT({})'.format(i+1,data['label'])
for i in range(np.prod(np.array(data['shape']))//3)]) # extend ASCII header with new labels
table.head_write()
# --------------- figure out size and grid ---------------------------------------------------------
table.data_readArray()
grid,size = damask.util.coordGridAndSize(table.data[:,table.label_indexrange(options.pos)])
# ------------------------------------------ process value field -----------------------------------
stack = [table.data]
for data in active:
# we need to reverse order here, because x is fastest,ie rightmost, but leftmost in our x,y,z notation
stack.append(divFFT(size[::-1],
table.data[:,table.label_indexrange(data['label'])].
reshape(grid[::-1].tolist()+data['shape'])))
# ------------------------------------------ output result -----------------------------------------
if len(stack) > 1: table.data = np.hstack(tuple(stack))
table.data_writeArray('%.12g')
# ------------------------------------------ output finalization -----------------------------------
table.close() # close input ASCII table (works for stdin)
for label in options.labels:
field = table.get_array(label)
shape = (3,) if np.prod(field.shape)//np.prod(grid) == 3 else (3,3) # vector or tensor
field = table.get_array(label).reshape(np.append(grid[::-1],shape))
table.add_array('divFFT({})'.format(label),
damask.grid_filters.divergence(size[::-1],field).reshape((-1,np.prod(shape)//3)),
scriptID+' '+' '.join(sys.argv[1:]))
table.to_ASCII(sys.stdout if name is None else name)

135
processing/post/addGradient.py
View File

@ -2,6 +2,7 @@
import os
import sys
from io import StringIO
from optparse import OptionParser
import numpy as np
@ -12,43 +13,6 @@ import damask
scriptName = os.path.splitext(os.path.basename(__file__))[0]
scriptID = ' '.join([scriptName,damask.version])
def merge_dicts(*dict_args):
"""Given any number of dicts, shallow copy and merge into a new dict, with precedence going to key value pairs in latter dicts."""
result = {}
for dictionary in dict_args:
result.update(dictionary)
return result
def gradFFT(geomdim,field):
"""Calculate gradient of a vector or scalar field by transforming into Fourier space."""
shapeFFT = np.array(np.shape(field))[0:3]
grid = np.array(np.shape(field)[2::-1])
N = grid.prod() # field size
n = np.array(np.shape(field)[3:]).prod() # data size
field_fourier = np.fft.rfftn(field,axes=(0,1,2),s=shapeFFT)
# differentiation in Fourier space
TWOPIIMG = 2.0j*np.pi
einsums = {
1:'ijkl,ijkm->ijkm', # scalar, 1 -> 3
3:'ijkl,ijkm->ijklm', # vector, 3 -> 3x3
}
k_sk = np.where(np.arange(grid[2])>grid[2]//2,np.arange(grid[2])-grid[2],np.arange(grid[2]))/geomdim[0]
if grid[2]%2 == 0: k_sk[grid[2]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011)
k_sj = np.where(np.arange(grid[1])>grid[1]//2,np.arange(grid[1])-grid[1],np.arange(grid[1]))/geomdim[1]
if grid[1]%2 == 0: k_sj[grid[1]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011)
k_si = np.arange(grid[0]//2+1)/geomdim[2]
kk, kj, ki = np.meshgrid(k_sk,k_sj,k_si,indexing = 'ij')
k_s = np.concatenate((ki[:,:,:,None],kj[:,:,:,None],kk[:,:,:,None]),axis = 3).astype('c16')
grad_fourier = np.einsum(einsums[n],field_fourier,k_s)*TWOPIIMG
return np.fft.irfftn(grad_fourier,axes=(0,1,2),s=shapeFFT).reshape([N,3*n])
# --------------------------------------------------------------------
# MAIN
@ -56,9 +20,7 @@ def gradFFT(geomdim,field):
parser = OptionParser(option_class=damask.extendableOption, usage='%prog options [ASCIItable(s)]', description = """
Add column(s) containing gradient of requested column(s).
Operates on periodic ordered three-dimensional data sets
of vector and scalar fields.
Operates on periodic ordered three-dimensional data sets of scalar and vector fields.
""", version = scriptID)
parser.add_option('-p','--pos','--periodiccellcenter',
@ -66,7 +28,7 @@ parser.add_option('-p','--pos','--periodiccellcenter',
type = 'string', metavar = 'string',
help = 'label of coordinates [%default]')
parser.add_option('-l','--label',
dest = 'data',
dest = 'labels',
action = 'extend', metavar = '<string LIST>',
help = 'label(s) of field values')
@ -74,85 +36,22 @@ parser.set_defaults(pos = 'pos',
)
(options,filenames) = parser.parse_args()
if options.data is None: parser.error('no data column specified.')
# --- define possible data types -------------------------------------------------------------------
datatypes = {
1: {'name': 'scalar',
'shape': [1],
},
3: {'name': 'vector',
'shape': [3],
},
}
# --- loop over input files ------------------------------------------------------------------------
if filenames == []: filenames = [None]
if options.labels is None: parser.error('no data column specified.')
for name in filenames:
try: table = damask.ASCIItable(name = name,buffered = False)
except: continue
damask.util.report(scriptName,name)
damask.util.report(scriptName,name)
# --- interpret header ----------------------------------------------------------------------------
table = damask.Table.from_ASCII(StringIO(''.join(sys.stdin.read())) if name is None else name)
grid,size = damask.util.coordGridAndSize(table.get_array(options.pos))
table.head_read()
remarks = []
errors = []
active = []
coordDim = table.label_dimension(options.pos)
if coordDim != 3:
errors.append('coordinates "{}" must be three-dimensional.'.format(options.pos))
else: coordCol = table.label_index(options.pos)
for me in options.data:
dim = table.label_dimension(me)
if dim in datatypes:
active.append(merge_dicts({'label':me},datatypes[dim]))
remarks.append('differentiating {} "{}"...'.format(datatypes[dim]['name'],me))
else:
remarks.append('skipping "{}" of dimension {}...'.format(me,dim) if dim != -1 else \
'"{}" not found...'.format(me) )
if remarks != []: damask.util.croak(remarks)
if errors != []:
damask.util.croak(errors)
table.close(dismiss = True)
continue
# ------------------------------------------ assemble header --------------------------------------
table.info_append(scriptID + '\t' + ' '.join(sys.argv[1:]))
for data in active:
table.labels_append(['{}_gradFFT({})'.format(i+1,data['label'])
for i in range(coordDim*np.prod(np.array(data['shape'])))]) # extend ASCII header with new labels
table.head_write()
# --------------- figure out size and grid ---------------------------------------------------------
table.data_readArray()
grid,size = damask.util.coordGridAndSize(table.data[:,table.label_indexrange(options.pos)])
# ------------------------------------------ process value field -----------------------------------
stack = [table.data]
for data in active:
# we need to reverse order here, because x is fastest,ie rightmost, but leftmost in our x,y,z notation
stack.append(gradFFT(size[::-1],
table.data[:,table.label_indexrange(data['label'])].
reshape(grid[::-1].tolist()+data['shape'])))
# ------------------------------------------ output result -----------------------------------------
if len(stack) > 1: table.data = np.hstack(tuple(stack))
table.data_writeArray('%.12g')
# ------------------------------------------ output finalization -----------------------------------
table.close() # close input ASCII table (works for stdin)
for label in options.labels:
field = table.get_array(label)
shape = (1,) if np.prod(field.shape)//np.prod(grid) == 1 else (3,) # scalar or vector
field = table.get_array(label).reshape(np.append(grid[::-1],shape))
table.add_array('gradFFT({})'.format(label),
damask.grid_filters.gradient(size[::-1],field).reshape((-1,np.prod(shape)*3)),
scriptID+' '+' '.join(sys.argv[1:]))
table.to_ASCII(sys.stdout if name is None else name)

63
python/damask/grid_filters.py
View File

@ -1,12 +1,8 @@
import numpy as np
def curl(size,field):
"""Calculate curl of a vector or tensor field in Fourier space."""
def __ks(size,field):
"""Get differential operator."""
grid = np.array(np.shape(field)[0:3])
n = np.array(np.shape(field)[3:]).prod() # data size
field_fourier = np.fft.rfftn(field,axes=(0,1,2))
k_sk = np.where(np.arange(grid[0])>grid[0]//2,np.arange(grid[0])-grid[0],np.arange(grid[0]))/size[0]
if grid[0]%2 == 0: k_sk[grid[0]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011)
@ -17,64 +13,47 @@ def curl(size,field):
k_si = np.arange(grid[2]//2+1)/size[2]
kk, kj, ki = np.meshgrid(k_sk,k_sj,k_si,indexing = 'ij')
k_s = np.concatenate((ki[:,:,:,None],kj[:,:,:,None],kk[:,:,:,None]),axis = 3).astype('c16')
return np.concatenate((ki[:,:,:,None],kj[:,:,:,None],kk[:,:,:,None]),axis = 3)
def curl(size,field):
"""Calculate curl of a vector or tensor field in Fourier space."""
n = np.prod(field.shape[3:])
k_s = __ks(size,field)
e = np.zeros((3, 3, 3))
e[0, 1, 2] = e[1, 2, 0] = e[2, 0, 1] = +1.0 # Levi-Civita symbol
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
return np.fft.irfftn(curl,axes=(0,1,2))
return np.fft.irfftn(curl,axes=(0,1,2),s=field.shape[0:3])
def divergence(size,field):
"""Calculate divergence of a vector or tensor field in Fourier space."""
grid = np.array(np.shape(field)[0:3])
n = np.array(np.shape(field)[3:]).prod() # data size
n = np.prod(field.shape[3:])
k_s = __ks(size,field)
field_fourier = np.fft.rfftn(field,axes=(0,1,2),s=grid)
field_fourier = np.fft.rfftn(field,axes=(0,1,2))
divergence = (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
k_sk = np.where(np.arange(grid[0])>grid[0]//2,np.arange(grid[0])-grid[0],np.arange(grid[0]))/size[0]
if grid[0]%2 == 0: k_sk[grid[0]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011)
k_sj = np.where(np.arange(grid[1])>grid[1]//2,np.arange(grid[1])-grid[1],np.arange(grid[1]))/size[1]
if grid[1]%2 == 0: k_sj[grid[1]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011)
k_si = np.arange(grid[2]//2+1)/size[2]
kk, kj, ki = np.meshgrid(k_sk,k_sj,k_si,indexing = 'ij')
k_s = np.concatenate((ki[:,:,:,None],kj[:,:,:,None],kk[:,:,:,None]),axis = 3).astype('c16')
divergence = (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_fourier,axes=(0,1,2),s=grid)
return np.fft.irfftn(divergence,axes=(0,1,2),s=field.shape[0:3])
def gradient(size,field):
"""Calculate gradient of a vector or scalar field in Fourier space."""
grid = np.array(np.shape(field)[2::-1])
n = np.array(np.shape(field)[3:]).prod() # data size
field_fourier = np.fft.rfftn(field,axes=(0,1,2),s=grid)
k_sk = np.where(np.arange(grid[0])>grid[0]//2,np.arange(grid[0])-grid[0],np.arange(grid[0]))/size[0]
if grid[0]%2 == 0: k_sk[grid[0]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011)
k_sj = np.where(np.arange(grid[1])>grid[1]//2,np.arange(grid[1])-grid[1],np.arange(grid[1]))/size[1]
if grid[1]%2 == 0: k_sj[grid[1]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011)
k_si = np.arange(grid[2]//2+1)/size[2]
kk, kj, ki = np.meshgrid(k_sk,k_sj,k_si,indexing = 'ij')
k_s = np.concatenate((ki[:,:,:,None],kj[:,:,:,None],kk[:,:,:,None]),axis = 3).astype('c16')
n = np.prod(field.shape[3:])
k_s = __ks(size,field)
field_fourier = np.fft.rfftn(field,axes=(0,1,2))
gradient = (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_fourier,axes=(0,1,2),s=grid)
return np.fft.irfftn(gradient,axes=(0,1,2),s=field.shape[0:3])
#--------------------------------------------------------------------------------------------------