Loading bubble-find/find-bubble-burst.ipynb +91 −19 Original line number Diff line number Diff line %% Cell type:code id:0e02bb89-8003-47a2-839f-58536b067490 tags: ``` python # Some parameters for the behavior of the extraction # Specifies the spacing of the sampling grid. lattice_parameter = 3.177 # The radius to use for a He splat He_radius = 0.01 # Minimum number of He atoms that have to escape for a bubble to be # considered burst. burst_size = 25 # Minimum fraction of He atoms in a bubble that have to escape for # the buble to be considered burst. burst_fraction = 0.75 # Number of time steps to pass to check for escaped atoms. time_to_escape = 10 # The maximum distance (squared) between bubble centers in two # different timesteps for them to be considered the same bubble. same_distance = 16 # Directory containing VTK files holding atoms. #data_path = '/Users/4d5/data/PSI/karl-hammond-2023/110-25x25nm/vtk-files' data_path = '/Users/4d5/data/PSI/karl-hammond-2023/110-25x25nm_detailed/vtk-files' ``` %% Cell type:code id:21fe4234-a349-402d-afdf-c9cb9a04f36a tags: ``` python import sys sys.path.append('/Users/4d5/builds/VTK/Release/lib/python3.11/site-packages') import vtk import numpy as np from vtk.util.numpy_support import vtk_to_numpy ``` %% Cell type:code id:ed2a82cd-2c92-4e73-a56b-06fd2ffd931b tags: ``` python class Bubble: '''Holds data for a bubble of atoms. Bubble is constructed with a vtkDataSet that contains the atoms of the bubble. Alternately, it can be constructed with a set of classified atoms and the identifier of the atom in the `RegionId` field (as comes from find_bubbles).''' def __init__(self, data, bubble_id = 0): if (bubble_id < 1): self.data = data else: threshold = vtk.vtkThreshold() threshold.SetInputData(data) threshold.SetInputArrayToProcess( 0, 0, 0, 'vtkDataObject::FIELD_ASSOCIATION_POINTS', 'RegionId') threshold.SetLowerThreshold(bubble_id - 0.1) threshold.SetUpperThreshold(bubble_id + 0.1) threshold.Update() self.data = threshold.GetOutput() self._center = None def get_number_of_atoms(self): return self.data.GetNumberOfPoints() def get_center(self): if not self._center: compute_center = vtk.vtkCenterOfMass() compute_center.SetInputData(self.data) compute_center.Update() self._center = compute_center.GetCenter() return self._center ``` %% Cell type:code id:122aa890-fdfe-4f24-9726-ec4fa0f9e8f6 tags: ``` python class HeAtoms: '''Holds information about one timestep of He atoms. This class is initialized by providing a VTK dataset representing a LAMMPS atom file containing an `id` field giving unique identifiers to atoms and a `type` field identifying the type of each atom (`type` == 2 is He atoms). The data needs no cell data. The constructor must also be given a timestep. Use the `ReadVTKFile()` method to load the data from a VTK data set. The `bubbles` field contains a list of `Bubble` objects holding the extracted bubbles. The `timestep` field contains the time of the atoms. The `filename` field provides the file the atoms came from, when available.''' def ReadVTKFile(filename): import re timestep_match = re.search(r'([0-9]+)\.vtk', filename) timestep = int(timestep_match.group(1)) reader = vtk.vtkDataSetReader() reader.SetFileName(filename) reader.Update() return HeAtoms(reader.GetOutput(), timestep, filename) def __init__(self, data, timestep, filename=None): self.timestep = timestep self.filename = filename # Many filters expect the data to have cells. Make one cell per point. tocloud = vtk.vtkConvertToPointCloud() tocloud.SetInputData(data) tocloud.SetCellGenerationMode(tocloud.VERTEX_CELLS) # Extract the He atoms. extract_he = vtk.vtkThreshold() extract_he.SetInputConnection(tocloud.GetOutputPort()) extract_he.SetInputArrayToProcess( 0, 0, 0, 'vtkDataObject::FIELD_ASSOCIATION_POINTS', 'type') extract_he.SetLowerThreshold(1.9) extract_he.SetUpperThreshold(2.1) # Create a density field of atoms by splatting the atoms into a grid. # Here we use `vtkGaussianSplatter`. If this is taking too long, it # is possible to speed things up using a `vtkFastSplatter`. bounds = data.GetBounds() sampling_resolution = ( int((bounds[1] - bounds[0]) / (lattice_parameter / 2)), int((bounds[3] - bounds[2]) / (lattice_parameter / 2)), int((bounds[5] - bounds[4]) / (lattice_parameter / 2))) splatter = vtk.vtkGaussianSplatter() splatter.SetInputConnection(extract_he.GetOutputPort()) splatter.SetSampleDimensions(sampling_resolution) splatter.SetRadius(He_radius) splatter.SetNormalWarping(0) splatter.SetAccumulationModeToSum() # Use an image connectivity filter to find regions with nearby atoms. # The filter will assign each connected region a unique ID and write # that to point data. connectivity = vtk.vtkImageConnectivityFilter() connectivity.SetInputConnection(splatter.GetOutputPort()) connectivity.SetLabelScalarTypeToInt() connectivity.SetLabelModeToSizeRank() #connectivity.SetLabelModeToSizeRank() # Lowering threshold to include regions to prevent missing atoms at edge # of bubble. connectivity.SetScalarRange(0.1, 100000000000) # Frustratingly, there appears to be a bug in `vtkImageConnectivityFilter` # that does not properly pass the origin and spacing of the image, which # means that it will no longer align with the atom data. Restore it to # the proper values. splatter.Update() splatter_output = splatter.GetOutput() reset_position = vtk.vtkImageChangeInformation() reset_position.SetInputConnection(connectivity.GetOutputPort()) reset_position.SetOutputOrigin(splatter_output.GetOrigin()) reset_position.SetOutputSpacing(splatter_output.GetSpacing()) # Sample the connectivity field back onto the atoms that generated them. # This will add a `RegionId` field to the atoms that identifes which # cluster each one belongs to. probe = vtk.vtkProbeFilter() probe.SetInputConnection(0, extract_he.GetOutputPort()) probe.SetInputConnection(1, reset_position.GetOutputPort()) probe.CategoricalDataOn() probe.PassPointArraysOn() connectivity.Update() bubble_sizes = connectivity.GetExtractedRegionSizes() probe.Update() self.atoms = probe.GetOutput() self.bubbles = [] for bubble_index in range(1, bubble_sizes.GetNumberOfValues()): if bubble_sizes.GetValue(bubble_index) < burst_size: break self.bubbles.append(Bubble(self.atoms, bubble_index)) for bubble_index in range(1, int(self.atoms.GetPointData(). GetArray('RegionId').GetRange()[1])): bubble = Bubble(self.atoms, bubble_index) if bubble.get_number_of_atoms() >= burst_size: self.bubbles.append(bubble) ``` %% Cell type:code id:034539e1-5b21-4952-ae11-eca00cd35283 tags: ``` python def find_burst_bubbles(reference_atoms, future_atoms): '''Given an `HeAtoms` object at a reference time and another such object at a future timestep, determine which bubbles in the reference time have burst. When a bubble bursts, the atoms become evacuated from their cavity into a vacuum and disappear from the simulation. When a large number of atoms in a bubble are not in the next timestep, that is indicitive of the bubble bursting. This function returns a list of `Bubble` objects that have been detected as burst.''' burst_bubbles = [] future_ids = \ vtk_to_numpy(future_atoms.atoms.GetPointData().GetArray('id')) for bubble in reference_atoms.bubbles: reference_ids = \ vtk_to_numpy(bubble.data.GetPointData().GetArray('id')) num_gone = np.isin(reference_ids, future_ids, assume_unique=True, invert=True).sum() fraction = float(num_gone)/len(reference_ids) if (num_gone >= burst_size) and (fraction >= burst_fraction): print(num_gone, fraction) #print(num_gone, fraction) burst_bubbles.append(bubble) return burst_bubbles ``` %% Cell type:code id:0f551511-82e4-4e98-8557-6315b7beacb3 tags: ``` python # Iterate over all the files in the data path and find potential bubble bursts. import queue bubble_queue = queue.Queue(time_to_escape - 1) print('begin_time,end_time,center_x,center_y,center_z,size') active_bursts = [] import glob for filename in sorted(glob.glob(data_path + '/*-0890*.vtk')): for filename in sorted(glob.glob(data_path + '/*.vtk')): next_atoms = HeAtoms.ReadVTKFile(filename) if bubble_queue.full(): reference_atoms = bubble_queue.get_nowait() burst_bubbles = find_burst_bubbles(reference_atoms, next_atoms) for bubble in burst_bubbles: print(reference_atoms.timestep, bubble.get_center(), filename) for bubble in find_burst_bubbles(reference_atoms, next_atoms): is_active = False for active_burst in active_bursts: bubble_center = bubble.get_center() active_center = active_burst['bubble'].get_center() distsquare = ( (bubble_center[0]-active_center[0])**2 + (bubble_center[1]-active_center[1])**2 + (bubble_center[2]-active_center[2])**2 ) if distsquare < same_distance: active_burst['endtime'] = next_atoms.timestep is_active = True if not is_active: active_bursts.append({ 'bubble': bubble, 'begintime' : reference_atoms.timestep, 'endtime' : next_atoms.timestep }) new_active = [] for active_burst in active_bursts: if active_burst['endtime'] < next_atoms.timestep: center = active_burst['bubble'].get_center() print('{},{},{:0.1f},{:0.1f},{:0.1f},{}'.format( active_burst['begintime'], active_burst['endtime'], center[0], center[1], center[2], active_burst['bubble'].data.GetNumberOfPoints())) else: new_active.append(active_burst) active_bursts = new_active bubble_queue.put_nowait(next_atoms) ``` %% Output 129 0.8164556962025317 89018 (219.2584626403036, 128.282757288293, 4.523309201847974) /Users/4d5/data/PSI/karl-hammond-2023/110-25x25nm_detailed/vtk-files/110-25x25nm-detailed-089027.vtk 133 0.8417721518987342 89019 (219.4156682461123, 128.26865285559546, 4.131269966311092) /Users/4d5/data/PSI/karl-hammond-2023/110-25x25nm_detailed/vtk-files/110-25x25nm-detailed-089028.vtk 134 0.8375 89020 (219.19135427474976, 128.24084725379944, 3.909063812252134) /Users/4d5/data/PSI/karl-hammond-2023/110-25x25nm_detailed/vtk-files/110-25x25nm-detailed-089029.vtk begin_time,end_time,center_x,center_y,center_x,size 84241,84258,96.9,88.0,2.1,109 85293,85302,170.9,113.4,2.6,29 86015,86029,88.6,176.7,6.9,32 86262,86271,47.9,2.6,3.6,29 86264,86274,47.9,2.7,3.8,28 86261,86277,47.7,244.9,2.2,32 86267,86278,48.0,2.4,3.6,29 86309,86325,61.8,217.1,1.0,56 86537,86553,120.5,94.7,0.3,42 86546,86561,188.8,132.3,3.5,60 87201,87210,223.5,53.3,5.4,31 87203,87214,223.4,53.2,5.4,30 87418,87430,39.9,122.3,3.0,36 87424,87433,40.1,122.9,3.3,27 87473,87488,106.1,163.6,1.6,78 89018,89029,219.3,128.3,4.5,158 90220,90229,204.4,72.4,2.2,30 90222,90232,204.5,72.6,2.2,30 90226,90237,204.4,72.8,2.0,29 90509,90518,10.3,86.5,2.6,100 90512,90521,10.7,86.7,2.5,100 91315,91324,37.1,138.5,1.7,35 91317,91326,37.3,138.8,2.0,37 91319,91328,37.1,138.7,1.5,36 91828,91837,68.2,154.2,17.1,1480 92003,92020,23.9,223.1,-0.0,119 93481,93498,153.7,227.3,2.5,35 94431,94440,45.6,63.9,14.9,1170 95034,95050,180.9,131.6,0.3,116 95299,95314,4.8,181.9,2.1,43 96158,96167,116.9,149.2,-1.2,32 96712,96723,229.0,79.9,-0.7,26 96716,96728,228.9,80.1,-0.5,26 96768,96777,44.8,192.5,-0.0,33 98265,98281,56.0,178.7,-4.3,37 98322,98338,178.4,190.1,18.6,1385 99089,99106,29.1,124.6,3.8,51 100375,100385,55.0,102.5,2.7,52 %% Cell type:code id:9dc7cc17-3cf3-4afd-a024-6ac6f7da8fbb tags: %% Cell type:code id:60b38426-7bc1-4739-a365-6eb921df59d7 tags: ``` python ``` Loading
bubble-find/find-bubble-burst.ipynb +91 −19 Original line number Diff line number Diff line %% Cell type:code id:0e02bb89-8003-47a2-839f-58536b067490 tags: ``` python # Some parameters for the behavior of the extraction # Specifies the spacing of the sampling grid. lattice_parameter = 3.177 # The radius to use for a He splat He_radius = 0.01 # Minimum number of He atoms that have to escape for a bubble to be # considered burst. burst_size = 25 # Minimum fraction of He atoms in a bubble that have to escape for # the buble to be considered burst. burst_fraction = 0.75 # Number of time steps to pass to check for escaped atoms. time_to_escape = 10 # The maximum distance (squared) between bubble centers in two # different timesteps for them to be considered the same bubble. same_distance = 16 # Directory containing VTK files holding atoms. #data_path = '/Users/4d5/data/PSI/karl-hammond-2023/110-25x25nm/vtk-files' data_path = '/Users/4d5/data/PSI/karl-hammond-2023/110-25x25nm_detailed/vtk-files' ``` %% Cell type:code id:21fe4234-a349-402d-afdf-c9cb9a04f36a tags: ``` python import sys sys.path.append('/Users/4d5/builds/VTK/Release/lib/python3.11/site-packages') import vtk import numpy as np from vtk.util.numpy_support import vtk_to_numpy ``` %% Cell type:code id:ed2a82cd-2c92-4e73-a56b-06fd2ffd931b tags: ``` python class Bubble: '''Holds data for a bubble of atoms. Bubble is constructed with a vtkDataSet that contains the atoms of the bubble. Alternately, it can be constructed with a set of classified atoms and the identifier of the atom in the `RegionId` field (as comes from find_bubbles).''' def __init__(self, data, bubble_id = 0): if (bubble_id < 1): self.data = data else: threshold = vtk.vtkThreshold() threshold.SetInputData(data) threshold.SetInputArrayToProcess( 0, 0, 0, 'vtkDataObject::FIELD_ASSOCIATION_POINTS', 'RegionId') threshold.SetLowerThreshold(bubble_id - 0.1) threshold.SetUpperThreshold(bubble_id + 0.1) threshold.Update() self.data = threshold.GetOutput() self._center = None def get_number_of_atoms(self): return self.data.GetNumberOfPoints() def get_center(self): if not self._center: compute_center = vtk.vtkCenterOfMass() compute_center.SetInputData(self.data) compute_center.Update() self._center = compute_center.GetCenter() return self._center ``` %% Cell type:code id:122aa890-fdfe-4f24-9726-ec4fa0f9e8f6 tags: ``` python class HeAtoms: '''Holds information about one timestep of He atoms. This class is initialized by providing a VTK dataset representing a LAMMPS atom file containing an `id` field giving unique identifiers to atoms and a `type` field identifying the type of each atom (`type` == 2 is He atoms). The data needs no cell data. The constructor must also be given a timestep. Use the `ReadVTKFile()` method to load the data from a VTK data set. The `bubbles` field contains a list of `Bubble` objects holding the extracted bubbles. The `timestep` field contains the time of the atoms. The `filename` field provides the file the atoms came from, when available.''' def ReadVTKFile(filename): import re timestep_match = re.search(r'([0-9]+)\.vtk', filename) timestep = int(timestep_match.group(1)) reader = vtk.vtkDataSetReader() reader.SetFileName(filename) reader.Update() return HeAtoms(reader.GetOutput(), timestep, filename) def __init__(self, data, timestep, filename=None): self.timestep = timestep self.filename = filename # Many filters expect the data to have cells. Make one cell per point. tocloud = vtk.vtkConvertToPointCloud() tocloud.SetInputData(data) tocloud.SetCellGenerationMode(tocloud.VERTEX_CELLS) # Extract the He atoms. extract_he = vtk.vtkThreshold() extract_he.SetInputConnection(tocloud.GetOutputPort()) extract_he.SetInputArrayToProcess( 0, 0, 0, 'vtkDataObject::FIELD_ASSOCIATION_POINTS', 'type') extract_he.SetLowerThreshold(1.9) extract_he.SetUpperThreshold(2.1) # Create a density field of atoms by splatting the atoms into a grid. # Here we use `vtkGaussianSplatter`. If this is taking too long, it # is possible to speed things up using a `vtkFastSplatter`. bounds = data.GetBounds() sampling_resolution = ( int((bounds[1] - bounds[0]) / (lattice_parameter / 2)), int((bounds[3] - bounds[2]) / (lattice_parameter / 2)), int((bounds[5] - bounds[4]) / (lattice_parameter / 2))) splatter = vtk.vtkGaussianSplatter() splatter.SetInputConnection(extract_he.GetOutputPort()) splatter.SetSampleDimensions(sampling_resolution) splatter.SetRadius(He_radius) splatter.SetNormalWarping(0) splatter.SetAccumulationModeToSum() # Use an image connectivity filter to find regions with nearby atoms. # The filter will assign each connected region a unique ID and write # that to point data. connectivity = vtk.vtkImageConnectivityFilter() connectivity.SetInputConnection(splatter.GetOutputPort()) connectivity.SetLabelScalarTypeToInt() connectivity.SetLabelModeToSizeRank() #connectivity.SetLabelModeToSizeRank() # Lowering threshold to include regions to prevent missing atoms at edge # of bubble. connectivity.SetScalarRange(0.1, 100000000000) # Frustratingly, there appears to be a bug in `vtkImageConnectivityFilter` # that does not properly pass the origin and spacing of the image, which # means that it will no longer align with the atom data. Restore it to # the proper values. splatter.Update() splatter_output = splatter.GetOutput() reset_position = vtk.vtkImageChangeInformation() reset_position.SetInputConnection(connectivity.GetOutputPort()) reset_position.SetOutputOrigin(splatter_output.GetOrigin()) reset_position.SetOutputSpacing(splatter_output.GetSpacing()) # Sample the connectivity field back onto the atoms that generated them. # This will add a `RegionId` field to the atoms that identifes which # cluster each one belongs to. probe = vtk.vtkProbeFilter() probe.SetInputConnection(0, extract_he.GetOutputPort()) probe.SetInputConnection(1, reset_position.GetOutputPort()) probe.CategoricalDataOn() probe.PassPointArraysOn() connectivity.Update() bubble_sizes = connectivity.GetExtractedRegionSizes() probe.Update() self.atoms = probe.GetOutput() self.bubbles = [] for bubble_index in range(1, bubble_sizes.GetNumberOfValues()): if bubble_sizes.GetValue(bubble_index) < burst_size: break self.bubbles.append(Bubble(self.atoms, bubble_index)) for bubble_index in range(1, int(self.atoms.GetPointData(). GetArray('RegionId').GetRange()[1])): bubble = Bubble(self.atoms, bubble_index) if bubble.get_number_of_atoms() >= burst_size: self.bubbles.append(bubble) ``` %% Cell type:code id:034539e1-5b21-4952-ae11-eca00cd35283 tags: ``` python def find_burst_bubbles(reference_atoms, future_atoms): '''Given an `HeAtoms` object at a reference time and another such object at a future timestep, determine which bubbles in the reference time have burst. When a bubble bursts, the atoms become evacuated from their cavity into a vacuum and disappear from the simulation. When a large number of atoms in a bubble are not in the next timestep, that is indicitive of the bubble bursting. This function returns a list of `Bubble` objects that have been detected as burst.''' burst_bubbles = [] future_ids = \ vtk_to_numpy(future_atoms.atoms.GetPointData().GetArray('id')) for bubble in reference_atoms.bubbles: reference_ids = \ vtk_to_numpy(bubble.data.GetPointData().GetArray('id')) num_gone = np.isin(reference_ids, future_ids, assume_unique=True, invert=True).sum() fraction = float(num_gone)/len(reference_ids) if (num_gone >= burst_size) and (fraction >= burst_fraction): print(num_gone, fraction) #print(num_gone, fraction) burst_bubbles.append(bubble) return burst_bubbles ``` %% Cell type:code id:0f551511-82e4-4e98-8557-6315b7beacb3 tags: ``` python # Iterate over all the files in the data path and find potential bubble bursts. import queue bubble_queue = queue.Queue(time_to_escape - 1) print('begin_time,end_time,center_x,center_y,center_z,size') active_bursts = [] import glob for filename in sorted(glob.glob(data_path + '/*-0890*.vtk')): for filename in sorted(glob.glob(data_path + '/*.vtk')): next_atoms = HeAtoms.ReadVTKFile(filename) if bubble_queue.full(): reference_atoms = bubble_queue.get_nowait() burst_bubbles = find_burst_bubbles(reference_atoms, next_atoms) for bubble in burst_bubbles: print(reference_atoms.timestep, bubble.get_center(), filename) for bubble in find_burst_bubbles(reference_atoms, next_atoms): is_active = False for active_burst in active_bursts: bubble_center = bubble.get_center() active_center = active_burst['bubble'].get_center() distsquare = ( (bubble_center[0]-active_center[0])**2 + (bubble_center[1]-active_center[1])**2 + (bubble_center[2]-active_center[2])**2 ) if distsquare < same_distance: active_burst['endtime'] = next_atoms.timestep is_active = True if not is_active: active_bursts.append({ 'bubble': bubble, 'begintime' : reference_atoms.timestep, 'endtime' : next_atoms.timestep }) new_active = [] for active_burst in active_bursts: if active_burst['endtime'] < next_atoms.timestep: center = active_burst['bubble'].get_center() print('{},{},{:0.1f},{:0.1f},{:0.1f},{}'.format( active_burst['begintime'], active_burst['endtime'], center[0], center[1], center[2], active_burst['bubble'].data.GetNumberOfPoints())) else: new_active.append(active_burst) active_bursts = new_active bubble_queue.put_nowait(next_atoms) ``` %% Output 129 0.8164556962025317 89018 (219.2584626403036, 128.282757288293, 4.523309201847974) /Users/4d5/data/PSI/karl-hammond-2023/110-25x25nm_detailed/vtk-files/110-25x25nm-detailed-089027.vtk 133 0.8417721518987342 89019 (219.4156682461123, 128.26865285559546, 4.131269966311092) /Users/4d5/data/PSI/karl-hammond-2023/110-25x25nm_detailed/vtk-files/110-25x25nm-detailed-089028.vtk 134 0.8375 89020 (219.19135427474976, 128.24084725379944, 3.909063812252134) /Users/4d5/data/PSI/karl-hammond-2023/110-25x25nm_detailed/vtk-files/110-25x25nm-detailed-089029.vtk begin_time,end_time,center_x,center_y,center_x,size 84241,84258,96.9,88.0,2.1,109 85293,85302,170.9,113.4,2.6,29 86015,86029,88.6,176.7,6.9,32 86262,86271,47.9,2.6,3.6,29 86264,86274,47.9,2.7,3.8,28 86261,86277,47.7,244.9,2.2,32 86267,86278,48.0,2.4,3.6,29 86309,86325,61.8,217.1,1.0,56 86537,86553,120.5,94.7,0.3,42 86546,86561,188.8,132.3,3.5,60 87201,87210,223.5,53.3,5.4,31 87203,87214,223.4,53.2,5.4,30 87418,87430,39.9,122.3,3.0,36 87424,87433,40.1,122.9,3.3,27 87473,87488,106.1,163.6,1.6,78 89018,89029,219.3,128.3,4.5,158 90220,90229,204.4,72.4,2.2,30 90222,90232,204.5,72.6,2.2,30 90226,90237,204.4,72.8,2.0,29 90509,90518,10.3,86.5,2.6,100 90512,90521,10.7,86.7,2.5,100 91315,91324,37.1,138.5,1.7,35 91317,91326,37.3,138.8,2.0,37 91319,91328,37.1,138.7,1.5,36 91828,91837,68.2,154.2,17.1,1480 92003,92020,23.9,223.1,-0.0,119 93481,93498,153.7,227.3,2.5,35 94431,94440,45.6,63.9,14.9,1170 95034,95050,180.9,131.6,0.3,116 95299,95314,4.8,181.9,2.1,43 96158,96167,116.9,149.2,-1.2,32 96712,96723,229.0,79.9,-0.7,26 96716,96728,228.9,80.1,-0.5,26 96768,96777,44.8,192.5,-0.0,33 98265,98281,56.0,178.7,-4.3,37 98322,98338,178.4,190.1,18.6,1385 99089,99106,29.1,124.6,3.8,51 100375,100385,55.0,102.5,2.7,52 %% Cell type:code id:9dc7cc17-3cf3-4afd-a024-6ac6f7da8fbb tags: %% Cell type:code id:60b38426-7bc1-4739-a365-6eb921df59d7 tags: ``` python ```