diff --git a/processing/post/addCurl.py b/processing/post/addCurl.py index b4dd465a9..2fcd107c0 100755 --- a/processing/post/addCurl.py +++ b/processing/post/addCurl.py @@ -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 = '', 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) diff --git a/processing/post/addDivergence.py b/processing/post/addDivergence.py index 2d6af2036..562ab7532 100755 --- a/processing/post/addDivergence.py +++ b/processing/post/addDivergence.py @@ -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 = '', 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) diff --git a/processing/post/addGradient.py b/processing/post/addGradient.py index 252b72eb8..d6b537ddd 100755 --- a/processing/post/addGradient.py +++ b/processing/post/addGradient.py @@ -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 = '', 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) diff --git a/python/damask/grid_filters.py b/python/damask/grid_filters.py index 69ee85033..c7e96f468 100644 --- a/python/damask/grid_filters.py +++ b/python/damask/grid_filters.py @@ -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]) #--------------------------------------------------------------------------------------------------