def PyExec(self):
self._runs = self.getProperty('RunNumbers').value
self._vanfile = self.getProperty('Vanadium').value
self._ecruns = self.getProperty('EmptyCanRunNumbers').value
self._ebins = (self.getProperty('EnergyBins').value).tolist()
self._qbins = (self.getProperty('MomentumTransferBins').value).tolist()
self._snorm = self.getProperty('NormalizeSlices').value
self._clean = self.getProperty('CleanWorkspaces').value
wn_sqes = self.getPropertyValue("OutputWorkspace")
# workspace names
prefix = ''
if self._clean:
prefix = '__'
# "wn" denotes workspace name
wn_data = prefix + 'data' # Accumulated data events
wn_data_mon = prefix + 'data_monitors' # Accumulated monitors for data
wn_van = prefix + 'vanadium' # White-beam vanadium
wn_van_st = prefix + 'vanadium_S_theta'
wn_reduced = prefix + 'reduced' # data after DGSReduction
wn_ste = prefix + 'S_theta_E' # data after grouping by theta angle
wn_sten = prefix + 'S_theta_E_normalized'
wn_steni = prefix + 'S_theta_E_interp'
wn_sqe = prefix + 'S_Q_E'
wn_sqeb = prefix + 'S_Q_E_binned'
wn_sqesn = prefix + wn_sqes + '_norm'
# Empty can files
wn_ec_data = prefix + 'ec_data' # Accumulated empty can data
wn_ec_data_mon = prefix + 'ec_data_monitors' # Accumulated monitors for empty can
wn_ec_reduced = prefix + 'ec_reduced' # empty can data after DGSReduction
wn_ec_ste = prefix + 'ec_S_theta_E' # empty can data after grouping by theta angle
# Save current configuration
facility = config['default.facility']
instrument = config['default.instrument']
datasearch = config["datasearch.searcharchive"]
# Allows searching for ARCS run numbers
config['default.facility'] = 'SNS'
config['default.instrument'] = 'ARCS'
config["datasearch.searcharchive"] = "On"
try:
# Load the vanadium file, assumed to be preprocessed, meaning that
# for every detector all events within a particular wide wavelength
# range have been rebinned into a single histogram
self._load(self._vanfile, wn_van)
# Check for white-beam vanadium, true if the vertical chopper is absent (vChTrans==2)
if api.mtd[wn_van].run().getProperty('vChTrans').value[0] != 2:
raise ValueError("White-vanadium is required")
# Load several event files into a single workspace. The nominal incident
# energy should be the same to avoid difference in energy resolution
self._load(self._runs, wn_data)
# Load empty can event files, if present
if self._ecruns:
self._load(self._ecruns, wn_ec_data)
finally:
# Recover the default configuration
config['default.facility'] = facility
config['default.instrument'] = instrument
config["datasearch.searcharchive"] = datasearch
# Obtain incident energy as the mean of the nominal Ei values.
# There is one nominal value for each run number.
ws_data = sapi.mtd[wn_data]
Ei = ws_data.getRun()['EnergyRequest'].getStatistics().mean
Ei_std = ws_data.getRun()['EnergyRequest'].getStatistics(
).standard_deviation
# Verify empty can runs were obtained at similar energy
if self._ecruns:
ws_ec_data = sapi.mtd[wn_ec_data]
ec_Ei = ws_ec_data.getRun()['EnergyRequest'].getStatistics().mean
if abs(Ei - ec_Ei) > Ei_std:
raise RuntimeError(
'Empty can runs were obtained at a significant' +
' different incident energy than the sample runs')
# Obtain energy range. If user did not supply a triad
# [Estart, Ewidth, Eend] but only Ewidth, then estimate
# Estart and End from the nominal energies
if len(self._ebins) == 1:
ws_data = sapi.mtd[wn_data]
Ei = ws_data.getRun()['EnergyRequest'].getStatistics().mean
self._ebins.insert(0, -0.5 * Ei) # prepend
self._ebins.append(0.95 * Ei) # append
# Enforce that the elastic energy (E=0) lies in the middle of the
# central bin with an appropriate small shift in the energy range
Ei_min_reduced = self._ebins[0] / self._ebins[1]
remainder = Ei_min_reduced - int(Ei_min_reduced)
if remainder >= 0.0:
erange_shift = self._ebins[1] * (0.5 - remainder)
else:
erange_shift = self._ebins[1] * (-0.5 - remainder)
self._ebins[0] += erange_shift # shift minimum energy
self._ebins[-1] += erange_shift # shift maximum energy
# Convert to energy transfer. Normalize by proton charge.
# The output workspace is S(detector-id,E)
factor = 0.1 # use a finer energy bin than the one passed (self._ebins[1])
Erange = '{0},{1},{2}'.format(self._ebins[0], factor * self._ebins[1],
self._ebins[2])
Ei_calc, T0 = sapi.GetEiT0atSNS(MonitorWorkspace=wn_data_mon,
IncidentEnergyGuess=Ei)
sapi.MaskDetectors(Workspace=wn_data,
MaskedWorkspace=wn_van) # Use vanadium mask
sapi.DgsReduction(SampleInputWorkspace=wn_data,
SampleInputMonitorWorkspace=wn_data_mon,
IncidentEnergyGuess=Ei_calc,
UseIncidentEnergyGuess=1,
TimeZeroGuess=T0,
EnergyTransferRange=Erange,
IncidentBeamNormalisation='ByCurrent',
OutputWorkspace=wn_reduced)
if self._ecruns:
sapi.MaskDetectors(Workspace=wn_ec_data, MaskedWorkspace=wn_van)
sapi.DgsReduction(SampleInputWorkspace=wn_ec_data,
SampleInputMonitorWorkspace=wn_ec_data_mon,
IncidentEnergyGuess=Ei_calc,
UseIncidentEnergyGuess=1,
TimeZeroGuess=T0,
EnergyTransferRange=Erange,
IncidentBeamNormalisation='ByCurrent',
OutputWorkspace=wn_ec_reduced)
# Obtain maximum and minimum |Q| values, as well as dQ if none passed
if len(self._qbins) < 3:
if not self._qbins:
# insert dQ if empty qbins. The minimal momentum transfer
# is the result on an event where the initial energy was
# Ei and the final energy was Ei+dE.
dE = self._ebins[1]
self._qbins.append(
numpy.sqrt((Ei + dE) / ENERGY_TO_WAVEVECTOR) -
numpy.sqrt(Ei / ENERGY_TO_WAVEVECTOR))
mins, maxs = sapi.ConvertToMDMinMaxLocal(wn_reduced,
Qdimensions='|Q|',
dEAnalysisMode='Direct')
self._qbins.insert(0, mins[0]) # prepend minimum Q
self._qbins.append(maxs[0]) # append maximum Q
# Delete sample and empty can event workspaces to free memory.
if self._clean:
sapi.DeleteWorkspace(wn_data)
if self._ecruns:
sapi.DeleteWorkspace(wn_ec_data)
# Convert to S(theta,E)
ki = numpy.sqrt(Ei / ENERGY_TO_WAVEVECTOR)
# If dE is the smallest energy transfer considered,
# then dQ/ki is the smallest dtheta (in radians)
dtheta = self._qbins[1] / ki * (180.0 / numpy.pi)
# Use a finer dtheta that the nominal smallest value
factor = 1. / 5 # a reasonable (heuristic) value
dtheta *= factor
# Fix: a very small dtheta (<0.15 degrees) prevents correct interpolation
dtheta = max(0.15, dtheta)
# Group detectors according to theta angle for the sample runs
group_file_os_handle, group_file_name = mkstemp(suffix='.xml')
group_file_handle = os.fdopen(group_file_os_handle, 'w')
sapi.GenerateGroupingPowder(InputWorkspace=wn_reduced,
AngleStep=dtheta,
GroupingFilename=group_file_name)
group_file_handle.close()
sapi.GroupDetectors(InputWorkspace=wn_reduced,
MapFile=group_file_name,
OutputWorkspace=wn_ste)
# Group detectors according to theta angle for the emtpy can run
if self._ecruns:
sapi.GroupDetectors(InputWorkspace=wn_ec_reduced,
MapFile=group_file_name,
OutputWorkspace=wn_ec_ste)
# Subtract the empty can from the can+sample
sapi.Minus(LHSWorkspace=wn_ste,
RHSWorkspace=wn_ec_ste,
OutputWorkspace=wn_ste)
# Normalize by the vanadium intensity, but before that we need S(theta)
# for the vanadium. Recall every detector has all energies into a single
# bin, so we get S(theta) instead of S(theta,E)
sapi.GroupDetectors(InputWorkspace=wn_van,
MapFile=group_file_name,
OutputWorkspace=wn_van_st)
# Divide by vanadium. Make sure it is integrated in the energy domain
sapi.Integration(wn_van_st, OutputWorkspace=wn_van_st)
sapi.Divide(wn_ste, wn_van_st, OutputWorkspace=wn_sten)
sapi.ClearMaskFlag(Workspace=wn_sten)
# Temporary file generated by GenerateGroupingPowder to be removed
os.remove(group_file_name) # no need for this file
os.remove(os.path.splitext(group_file_name)[0] + ".par")
max_i_theta = 0.0
min_i_theta = 0.0
# Linear interpolation for those theta values with low intensity
# First, find minimum theta index with a non-zero histogram
ws_sten = sapi.mtd[wn_sten]
for i_theta in range(ws_sten.getNumberHistograms()):
if ws_sten.dataY(i_theta).any():
min_i_theta = i_theta
break
# second, find maximum theta with a non-zero histogram
for i_theta in range(ws_sten.getNumberHistograms() - 1, -1, -1):
if ws_sten.dataY(i_theta).any():
max_i_theta = i_theta
break
# Scan a range of theta angles and apply interpolation to those theta angles
# with considerably low intensity (gaps)
delta_theta = max_i_theta - min_i_theta
gaps = self._findGaps(wn_sten, int(min_i_theta + 0.1 * delta_theta),
int(max_i_theta - 0.1 * delta_theta))
sapi.CloneWorkspace(InputWorkspace=wn_sten, OutputWorkspace=wn_steni)
for gap in gaps:
self._interpolate(wn_steni, gap) # interpolate this gap
# Convert S(theta,E) to S(Q,E), then rebin in |Q| and E to MD workspace
sapi.ConvertToMD(InputWorkspace=wn_steni,
QDimensions='|Q|',
dEAnalysisMode='Direct',
OutputWorkspace=wn_sqe)
Qmin = self._qbins[0]
Qmax = self._qbins[-1]
dQ = self._qbins[1]
Qrange = '|Q|,{0},{1},{2}'.format(Qmin, Qmax, int((Qmax - Qmin) / dQ))
Ei_min = self._ebins[0]
Ei_max = self._ebins[-1]
dE = self._ebins[1]
deltaErange = 'DeltaE,{0},{1},{2}'.format(Ei_min, Ei_max,
int((Ei_max - Ei_min) / dE))
sapi.BinMD(InputWorkspace=wn_sqe,
AxisAligned=1,
AlignedDim0=Qrange,
AlignedDim1=deltaErange,
OutputWorkspace=wn_sqeb)
# Slice the data by transforming to a Matrix2Dworkspace,
# with deltaE along the vertical axis
sapi.ConvertMDHistoToMatrixWorkspace(
InputWorkspace=wn_sqeb,
Normalization='NumEventsNormalization',
OutputWorkspace=wn_sqes)
# Ensure correct units
sapi.mtd[wn_sqes].getAxis(0).setUnit("MomentumTransfer")
sapi.mtd[wn_sqes].getAxis(1).setUnit("DeltaE")
# Shift the energy axis, since the reported values should be the center
# of the bins, instead of the minimum bin boundary
ws_sqes = sapi.mtd[wn_sqes]
Eaxis = ws_sqes.getAxis(1)
e_shift = self._ebins[1] / 2.0
for i in range(Eaxis.length()):
Eaxis.setValue(i, Eaxis.getValue(i) + e_shift)
# Normalize each slice, if requested
if self._snorm:
sapi.Integration(InputWorkspace=wn_sqes, OutputWorkspace=wn_sqesn)
sapi.Divide(LHSWorkspace=wn_sqes,
RHSWorkspace=wn_sqesn,
OutputWorkspace=wn_sqes)
# Clean up workspaces from intermediate steps
if self._clean:
for name in (wn_van, wn_reduced, wn_ste, wn_van_st, wn_sten,
wn_steni, wn_sqe, wn_sqeb, wn_sqesn,
'PreprocessedDetectorsWS'):
if sapi.mtd.doesExist(name):
sapi.DeleteWorkspace(name)
# Ouput some info as a Notice in the log
ebins = ', '.join(['{0:.2f}'.format(x) for x in self._ebins])
qbins = ', '.join(['{0:.2f}'.format(x) for x in self._qbins])
tbins = '{0:.2f} {1:.2f} {2:.2f}'.format(min_i_theta * dtheta, dtheta,
max_i_theta * dtheta)
message = '\n****** SOME OUTPUT INFORMATION ***' + \
'\nEnergy bins: ' + ebins + \
'\nQ bins: ' + qbins + \
'\nTheta bins: '+tbins
kapi.logger.notice(message)
self.setProperty("OutputWorkspace", sapi.mtd[wn_sqes])
def PyExec(self):
config['default.facility'] = 'SNS'
config['default.instrument'] = 'ARCS'
self._runs = self.getProperty('RunNumbers').value
self._vanfile = self.getProperty('Vanadium').value
self._ecruns = self.getProperty('EmptyCanRunNumbers').value
self._ebins_str = self.getProperty('EnergyBins').value
self._qbins_str = self.getProperty('MomentumTransferBins').value
self._snorm = self.getProperty('NormalizeSlices').value
self._clean = self.getProperty('CleanWorkspaces').value
wn_sqes = self.getPropertyValue("OutputWorkspace")
# workspace names
prefix = ''
if self._clean:
prefix = '__'
# Sample files
wn_data = prefix + 'data'
wn_van = prefix + 'vanadium'
wn_reduced = prefix + 'reduced'
wn_ste = prefix + 'S_theta_E'
wn_van_st = prefix + 'vanadium_S_theta'
wn_sten = prefix + 'S_theta_E_normalized'
wn_steni = prefix + 'S_theta_E_normalized_interp'
wn_sqe = prefix + 'S_Q_E'
wn_sqeb = prefix + 'S_Q_E_binned'
wn_sqesn = prefix + wn_sqes + '_norm'
# Empty can files
wn_ec_data = prefix + 'ec_data'
wn_ec_reduced = prefix + 'ec_reduced'
wn_ec_ste = prefix + 'ec_S_theta_E'
datasearch = config["datasearch.searcharchive"]
if datasearch != "On":
config["datasearch.searcharchive"] = "On"
# Load several event files into a sinle workspace. The nominal incident
# energy should be the same to avoid difference in energy resolution
api.Load(Filename=self._runs, OutputWorkspace=wn_data)
# Load the vanadium file, assume to be preprocessed, meaning that
# for every detector all events whithin a particular wide wavelength
# range have been rebinned into a single histogram
api.Load(Filename=self._vanfile, OutputWorkspace=wn_van)
# Load empty can event files, if present
if self._ecruns:
api.Load(Filename=self._ecruns, OutputWorkspace=wn_ec_data)
# Retrieve the mask from the vanadium workspace, and apply it to the data
# (and empty can, if submitted)
api.MaskDetectors(Workspace=wn_data, MaskedWorkspace=wn_van)
if self._ecruns:
api.MaskDetectors(Workspace=wn_ec_data, MaskedWorkspace=wn_van)
# Obtain incident energy as the mean of the nominal Ei values.
# There is one nominal value per events file.
ws_data = api.mtd[wn_data]
Ei = ws_data.getRun()['EnergyRequest'].getStatistics().mean
Ei_std = ws_data.getRun()['EnergyRequest'].getStatistics(
).standard_deviation
# Verify empty can runs were obtained at similar energy
if self._ecruns:
ws_ec_data = api.mtd[wn_ec_data]
ec_Ei = ws_ec_data.getRun()['EnergyRequest'].getStatistics().mean
if abs(Ei - ec_Ei) > Ei_std:
raise RuntimeError(
'Empty can runs were obtained at a significant' +
' different incident energy than the sample runs')
# Obtain energy range
self._ebins = [
float(x)
for x in re.compile(r'\d+[\.\d+]*').findall(self._ebins_str)
]
if len(self._ebins) == 1:
ws_data = api.mtd[wn_data]
Ei = ws_data.getRun()['EnergyRequest'].getStatistics().mean
self._ebins.insert(0, -0.5 * Ei) # prepend
self._ebins.append(0.95 * Ei) # append
# Enforce that the elastic energy (E=0) lies in the middle of the
# central bin with an appropriate small shift in the energy range
Ei_min_reduced = self._ebins[0] / self._ebins[1]
remainder = Ei_min_reduced - int(Ei_min_reduced)
if remainder >= 0.0:
erange_shift = self._ebins[1] * (0.5 - remainder)
else:
erange_shift = self._ebins[1] * (-0.5 - remainder)
self._ebins[0] += erange_shift # shift minimum energy
self._ebins[-1] += erange_shift # shift maximum energy
# Convert to energy transfer. Normalize by proton charge.
# The output workspace is S(detector-id,E)
factor = 0.1 # a fine energy bin
Erange = '{0},{1},{2}'.format(self._ebins[0], factor * self._ebins[1],
self._ebins[2])
api.DgsReduction(SampleInputWorkspace=wn_data,
EnergyTransferRange=Erange,
OutputWorkspace=wn_reduced)
if self._ecruns:
api.DgsReduction(SampleInputWorkspace=wn_ec_data,
EnergyTransferRange=Erange,
IncidentBeamNormalisation='ByCurrent',
OutputWorkspace=wn_ec_reduced)
# Obtain maximum and minimum |Q| values, as well as dQ if none passed
self._qbins = [
float(x)
for x in re.compile(r'\d+[\.\d+]*').findall(self._qbins_str)
]
if len(self._qbins) < 3:
if not self._qbins:
# insert dQ if empty qbins
dE = self._ebins[1]
self._qbins.append(
numpy.sqrt((Ei + dE) / ENERGY_TO_WAVEVECTOR) -
numpy.sqrt(Ei / ENERGY_TO_WAVEVECTOR))
mins, maxs = api.ConvertToMDMinMaxLocal(wn_reduced,
Qdimensions='|Q|',
dEAnalysisMode='Direct')
self._qbins.insert(0, mins[0]) # prepend minimum Q
self._qbins.append(maxs[0]) # append maximum Q
# Clean up the events files. They take a lot of space in memory
api.DeleteWorkspace(wn_data)
if self._ecruns:
api.DeleteWorkspace(wn_ec_data)
# Convert to S(theta,E)
ki = numpy.sqrt(Ei / ENERGY_TO_WAVEVECTOR)
factor = 1. / 5 # a reasonable (heuristic) value
# If dE is the smallest energy transfer considered,
# then dQ/ki is the smallest dtheta (in radians)
dtheta = factor * self._qbins[1] / ki * (180.0 / numpy.pi)
# very small dtheta (<0.15 degrees) prevents interpolation
dtheta = max(0.15, dtheta)
group_file_os_handle, group_file_name = mkstemp(suffix='.xml')
group_file_handle = os.fdopen(group_file_os_handle, 'w')
api.GenerateGroupingPowder(InputWorkspace=wn_reduced,
AngleStep=dtheta,
GroupingFilename=group_file_name)
group_file_handle.close()
api.GroupDetectors(InputWorkspace=wn_reduced,
MapFile=group_file_name,
OutputWorkspace=wn_ste)
if self._ecruns:
api.GroupDetectors(InputWorkspace=wn_ec_reduced,
MapFile=group_file_name,
OutputWorkspace=wn_ec_ste)
# Substract the empty can from the can+sample
api.Minus(LHSWorkspace=wn_ste,
RHSWorkspace=wn_ec_ste,
OutputWorkspace=wn_ste)
# Normalize by the vanadium intensity, but before that we need S(theta)
# for the vanadium. Recall every detector has all energies into a single
# bin, so we get S(theta) instead of S(theta,E)
api.GroupDetectors(InputWorkspace=wn_van,
MapFile=group_file_name,
OutputWorkspace=wn_van_st)
os.remove(group_file_name) # no need for this file
api.Divide(wn_ste, wn_van_st, OutputWorkspace=wn_sten)
api.ClearMaskFlag(Workspace=wn_sten)
max_i_theta = 0.0
min_i_theta = 0.0
# Linear interpolation
# First, find minimum theta index with a non-zero histogram
ws_sten = api.mtd[wn_sten]
for i_theta in range(ws_sten.getNumberHistograms()):
if ws_sten.dataY(i_theta).any():
min_i_theta = i_theta
break
# second, find maximum theta with a non-zero histogram
for i_theta in range(ws_sten.getNumberHistograms() - 1, -1, -1):
if ws_sten.dataY(i_theta).any():
max_i_theta = i_theta
break
# Scan the region [min_i_theta, max_i_theta] and apply interpolation to
# theta angles with no signal whatsoever, S(theta*, E)=0.0 for all energies
api.CloneWorkspace(InputWorkspace=wn_sten, OutputWorkspace=wn_steni)
ws_steni = api.mtd[wn_steni]
i_theta = 1 + min_i_theta
while i_theta < max_i_theta:
if not ws_steni.dataY(i_theta).any():
nonnull_i_theta_start = i_theta - 1 # angle index of non-null histogram
# scan until we find a non-null histogram
while not ws_steni.dataY(i_theta).any():
i_theta += 1
nonnull_i_theta_end = i_theta # angle index of non-null histogram
# The range [1+nonnull_i_theta_start, nonnull_i_theta_end]
# contains only null-histograms. Interpolate!
y_start = ws_steni.dataY(nonnull_i_theta_start)
y_end = ws_steni.dataY(nonnull_i_theta_end)
intercept = y_start
slope = (y_end - y_start) / (nonnull_i_theta_end -
nonnull_i_theta_start)
for null_i_theta in range(1 + nonnull_i_theta_start,
nonnull_i_theta_end):
ws_steni.dataY(null_i_theta)[:] = intercept + slope * (
null_i_theta - nonnull_i_theta_start)
i_theta += 1
# Convert S(theta,E) to S(Q,E), then rebin in |Q| and E to MD workspace
api.ConvertToMD(InputWorkspace=wn_steni,
QDimensions='|Q|',
dEAnalysisMode='Direct',
OutputWorkspace=wn_sqe)
Qmin = self._qbins[0]
Qmax = self._qbins[-1]
dQ = self._qbins[1]
Qrange = '|Q|,{0},{1},{2}'.format(Qmin, Qmax, int((Qmax - Qmin) / dQ))
Ei_min = self._ebins[0]
Ei_max = self._ebins[-1]
dE = self._ebins[1]
deltaErange = 'DeltaE,{0},{1},{2}'.format(Ei_min, Ei_max,
int((Ei_max - Ei_min) / dE))
api.BinMD(InputWorkspace=wn_sqe,
AxisAligned=1,
AlignedDim0=Qrange,
AlignedDim1=deltaErange,
OutputWorkspace=wn_sqeb)
# Slice the data by transforming to a Matrix2Dworkspace, with deltaE along the vertical axis
api.ConvertMDHistoToMatrixWorkspace(
InputWorkspace=wn_sqeb,
Normalization='NumEventsNormalization',
OutputWorkspace=wn_sqes)
# Shift the energy axis, since the reported values should be the center
# of the bins, instead of the minimum bin boundary
ws_sqes = api.mtd[wn_sqes]
Eaxis = ws_sqes.getAxis(1)
e_shift = self._ebins[1] / 2.0
for i in range(Eaxis.length()):
Eaxis.setValue(i, Eaxis.getValue(i) + e_shift)
# Normalize each slice
if self._snorm:
api.Integration(InputWorkspace=wn_sqes, OutputWorkspace=wn_sqesn)
api.Divide(LHSWorkspace=wn_sqes,
RHSWorkspace=wn_sqesn,
OutputWorkspace=wn_sqes)
# Clean up workspaces from intermediate steps
if self._clean:
for name in (wn_van, wn_reduced, wn_ste, wn_van_st, wn_sten,
wn_steni, wn_sqe, wn_sqeb, wn_sqesn):
api.DeleteWorkspace(name)
if api.mtd.doesExist('PreprocessedDetectorsWS'):
api.DeleteWorkspace('PreprocessedDetectorsWS')
# Ouput some info
message = '\n****** SOME OUTPUT INFORMATION ***' + \
'\nEnergy bins: ' + ', '.join(['{0:.2f}'.format(x) for x in self._ebins]) + \
'\nQ bins: ' + ', '.join(['{0:.2f}'.format(x) for x in self._qbins]) + \
'\nTheta bins: {0:.2f} {1:.2f} {2:.2f}'.format(min_i_theta * dtheta, dtheta, max_i_theta * dtheta)
logger.notice(message)
self.setProperty("OutputWorkspace", api.mtd[wn_sqes])