def interpolate(cube, sample_points, method=None):
"""
Extract a sub-cube at the given n-dimensional points.
Args:
* cube
The source Cube.
* sample_points
A sequence of coordinate (name) - values pairs.
Kwargs:
* method
Request "linear" interpolation (default) or "nearest" neighbour.
Only nearest neighbour is available when specifying multi-dimensional
coordinates.
For example::
sample_points = [('latitude', [45, 45, 45]),
('longitude', [-60, -50, -40])]
interpolated_cube = interpolate(cube, sample_points)
"""
if method not in [None, "linear", "nearest"]:
raise ValueError("Unhandled interpolation specified : %s" % method)
# Convert any coordinate names to coords
points = []
for coord, values in sample_points:
if isinstance(coord, six.string_types):
coord = cube.coord(coord)
points.append((coord, values))
sample_points = points
# Do all value sequences have the same number of values?
coord, values = sample_points[0]
trajectory_size = len(values)
for coord, values in sample_points[1:]:
if len(values) != trajectory_size:
raise ValueError('Lengths of coordinate values are inconsistent.')
# Which dimensions are we squishing into the last dimension?
squish_my_dims = set()
for coord, values in sample_points:
dims = cube.coord_dims(coord)
for dim in dims:
squish_my_dims.add(dim)
# Derive the new cube's shape by filtering out all the dimensions we're
# about to sample,
# and then adding a new dimension to accommodate all the sample points.
remaining = [(dim, size) for dim, size in enumerate(cube.shape)
if dim not in squish_my_dims]
new_data_shape = [size for dim, size in remaining]
new_data_shape.append(trajectory_size)
# Start with empty data and then fill in the "column" of values for each
# trajectory point.
new_cube = iris.cube.Cube(np.empty(new_data_shape))
new_cube.metadata = cube.metadata
# Derive the mapping from the non-trajectory source dimensions to their
# corresponding destination dimensions.
remaining_dims = [dim for dim, size in remaining]
dimension_remap = {dim: i for i, dim in enumerate(remaining_dims)}
# Record a mapping from old coordinate IDs to new coordinates,
# for subsequent use in creating updated aux_factories.
coord_mapping = {}
# Create all the non-squished coords
for coord in cube.dim_coords:
src_dims = cube.coord_dims(coord)
if squish_my_dims.isdisjoint(src_dims):
dest_dims = [dimension_remap[dim] for dim in src_dims]
new_coord = coord.copy()
new_cube.add_dim_coord(new_coord, dest_dims)
coord_mapping[id(coord)] = new_coord
for coord in cube.aux_coords:
src_dims = cube.coord_dims(coord)
if squish_my_dims.isdisjoint(src_dims):
dest_dims = [dimension_remap[dim] for dim in src_dims]
new_coord = coord.copy()
new_cube.add_aux_coord(new_coord, dest_dims)
coord_mapping[id(coord)] = new_coord
# Create all the squished (non derived) coords, not filled in yet.
trajectory_dim = len(remaining_dims)
for coord in cube.dim_coords + cube.aux_coords:
src_dims = cube.coord_dims(coord)
if not squish_my_dims.isdisjoint(src_dims):
points = np.array([coord.points.flatten()[0]] * trajectory_size)
new_coord = iris.coords.AuxCoord(points,
standard_name=coord.standard_name,
long_name=coord.long_name,
units=coord.units,
bounds=None,
attributes=coord.attributes,
coord_system=coord.coord_system)
new_cube.add_aux_coord(new_coord, trajectory_dim)
coord_mapping[id(coord)] = new_coord
for factory in cube.aux_factories:
new_cube.add_aux_factory(factory.updated(coord_mapping))
# Are the given coords all 1-dimensional? (can we do linear interp?)
for coord, values in sample_points:
if coord.ndim > 1:
if method == "linear":
msg = "Cannot currently perform linear interpolation for " \
"multi-dimensional coordinates."
raise iris.exceptions.CoordinateMultiDimError(msg)
method = "nearest"
break
if method in ["linear", None]:
for i in range(trajectory_size):
point = [(coord, values[i]) for coord, values in sample_points]
column = linear_regrid(cube, point)
new_cube.data[..., i] = column.data
# Fill in the empty squashed (non derived) coords.
for column_coord in column.dim_coords + column.aux_coords:
src_dims = cube.coord_dims(column_coord)
if not squish_my_dims.isdisjoint(src_dims):
if len(column_coord.points) != 1:
msg = "Expected to find exactly one point. Found {}."
raise Exception(msg.format(column_coord.points))
new_cube.coord(column_coord.name()).points[i] = \
column_coord.points[0]
elif method == "nearest":
# Use a cache with _nearest_neighbour_indices_ndcoords()
cache = {}
column_indexes = _nearest_neighbour_indices_ndcoords(cube,
sample_points,
cache=cache)
# Construct "fancy" indexes, so we can create the result data array in
# a single numpy indexing operation.
# ALSO: capture the index range in each dimension, so that we can fetch
# only a required (square) sub-region of the source data.
fancy_source_indices = []
region_slices = []
n_index_length = len(column_indexes[0])
dims_reduced = [False] * n_index_length
for i_ind in range(n_index_length):
contents = [column_index[i_ind] for column_index in column_indexes]
each_used = [content != slice(None) for content in contents]
if np.all(each_used):
# This dimension is addressed : use a list of indices.
dims_reduced[i_ind] = True
# Select the region by min+max indices.
start_ind = np.min(contents)
stop_ind = 1 + np.max(contents)
region_slice = slice(start_ind, stop_ind)
# Record point indices with start subtracted from all of them.
fancy_index = list(np.array(contents) - start_ind)
elif not np.any(each_used):
# This dimension is not addressed by the operation.
# Use a ":" as the index.
fancy_index = slice(None)
# No sub-region selection for this dimension.
region_slice = slice(None)
else:
# Should really never happen, if _ndcoords is right.
msg = ('Internal error in trajectory interpolation : point '
'selection indices should all have the same form.')
raise ValueError(msg)
fancy_source_indices.append(fancy_index)
region_slices.append(region_slice)
# Fetch the required (square-section) region of the source data.
# NOTE: This is not quite as good as only fetching the individual
# points used, but it avoids creating a sub-cube for each point,
# which is very slow, especially when points are re-used a lot ...
source_area_indices = tuple(region_slices)
source_data = cube[source_area_indices].data
# Transpose source data before indexing it to get the final result.
# Because.. the fancy indexing will replace the indexed (horizontal)
# dimensions with a new single dimension over trajectory points.
# Move those dimensions to the end *first* : this ensures that the new
# dimension also appears at the end, which is where we want it.
# Make a list of dims with the reduced ones last.
dims_reduced = np.array(dims_reduced)
dims_order = np.arange(n_index_length)
dims_order = np.concatenate(
(dims_order[~dims_reduced], dims_order[dims_reduced]))
# Rearrange the data dimensions and the fancy indices into that order.
source_data = source_data.transpose(dims_order)
fancy_source_indices = [
fancy_source_indices[i_dim] for i_dim in dims_order
]
# Apply the fancy indexing to get all the result data points.
source_data = source_data[fancy_source_indices]
# "Fix" problems with missing datapoints producing odd values
# when copied from a masked into an unmasked array.
# TODO: proper masked data handling.
if np.ma.isMaskedArray(source_data):
# This is **not** proper mask handling, because we cannot produce a
# masked result, but it ensures we use a "filled" version of the
# input in this case.
source_data = source_data.filled()
new_cube.data[:] = source_data
# NOTE: we assign to "new_cube.data[:]" and *not* just "new_cube.data",
# because the existing code produces a default dtype from 'np.empty'
# instead of preserving the input dtype.
# TODO: maybe this should be fixed -- i.e. to preserve input dtype ??
# Fill in the empty squashed (non derived) coords.
column_coords = [
coord for coord in cube.dim_coords + cube.aux_coords
if not squish_my_dims.isdisjoint(cube.coord_dims(coord))
]
new_cube_coords = [
new_cube.coord(column_coord.name())
for column_coord in column_coords
]
all_point_indices = np.array(column_indexes)
single_point_test_cube = cube[column_indexes[0]]
for new_cube_coord, src_coord in zip(new_cube_coords, column_coords):
# Check structure of the indexed coord (at one selected point).
point_coord = single_point_test_cube.coord(src_coord)
if len(point_coord.points) != 1:
msg = ('Coord {} at one x-y position has the shape {}, '
'instead of being a single point. ')
raise ValueError(msg.format(src_coord.name(), src_coord.shape))
# Work out which indices apply to the input coord.
# NOTE: we know how to index the source cube to get a cube with a
# single point for each coord, but this is very inefficient.
# So here, we translate cube indexes into *coord* indexes.
src_coord_dims = cube.coord_dims(src_coord)
fancy_coord_index_arrays = [
list(all_point_indices[:, src_dim])
for src_dim in src_coord_dims
]
# Fill the new coord with all the correct points from the old one.
new_cube_coord.points = src_coord.points[fancy_coord_index_arrays]
# NOTE: the new coords do *not* have bounds.
return new_cube
def interpolate(cube, sample_points, method=None):
"""
Extract a sub-cube at the given n-dimensional points.
Args:
* cube
The source Cube.
* sample_points
A sequence of coordinate (name) - values pairs.
Kwargs:
* method
Request "linear" interpolation (default) or "nearest" neighbour.
Only nearest neighbour is available when specifying multi-dimensional
coordinates.
For example::
sample_points = [('latitude', [45, 45, 45]),
('longitude', [-60, -50, -40])]
interpolated_cube = interpolate(cube, sample_points)
"""
if method not in [None, "linear", "nearest"]:
raise ValueError("Unhandled interpolation specified : %s" % method)
# Convert any coordinate names to coords
points = []
for coord, values in sample_points:
if isinstance(coord, six.string_types):
coord = cube.coord(coord)
points.append((coord, values))
sample_points = points
# Do all value sequences have the same number of values?
coord, values = sample_points[0]
trajectory_size = len(values)
for coord, values in sample_points[1:]:
if len(values) != trajectory_size:
raise ValueError('Lengths of coordinate values are inconsistent.')
# Which dimensions are we squishing into the last dimension?
squish_my_dims = set()
for coord, values in sample_points:
dims = cube.coord_dims(coord)
for dim in dims:
squish_my_dims.add(dim)
# Derive the new cube's shape by filtering out all the dimensions we're
# about to sample,
# and then adding a new dimension to accommodate all the sample points.
remaining = [(dim, size) for dim, size in enumerate(cube.shape) if dim
not in squish_my_dims]
new_data_shape = [size for dim, size in remaining]
new_data_shape.append(trajectory_size)
# Start with empty data and then fill in the "column" of values for each
# trajectory point.
new_cube = iris.cube.Cube(np.empty(new_data_shape))
new_cube.metadata = cube.metadata
# Derive the mapping from the non-trajectory source dimensions to their
# corresponding destination dimensions.
remaining_dims = [dim for dim, size in remaining]
dimension_remap = {dim: i for i, dim in enumerate(remaining_dims)}
# Record a mapping from old coordinate IDs to new coordinates,
# for subsequent use in creating updated aux_factories.
coord_mapping = {}
# Create all the non-squished coords
for coord in cube.dim_coords:
src_dims = cube.coord_dims(coord)
if squish_my_dims.isdisjoint(src_dims):
dest_dims = [dimension_remap[dim] for dim in src_dims]
new_coord = coord.copy()
new_cube.add_dim_coord(new_coord, dest_dims)
coord_mapping[id(coord)] = new_coord
for coord in cube.aux_coords:
src_dims = cube.coord_dims(coord)
if squish_my_dims.isdisjoint(src_dims):
dest_dims = [dimension_remap[dim] for dim in src_dims]
new_coord = coord.copy()
new_cube.add_aux_coord(new_coord, dest_dims)
coord_mapping[id(coord)] = new_coord
# Create all the squished (non derived) coords, not filled in yet.
trajectory_dim = len(remaining_dims)
for coord in cube.dim_coords + cube.aux_coords:
src_dims = cube.coord_dims(coord)
if not squish_my_dims.isdisjoint(src_dims):
points = np.array([coord.points.flatten()[0]] * trajectory_size)
new_coord = iris.coords.AuxCoord(points,
standard_name=coord.standard_name,
long_name=coord.long_name,
units=coord.units,
bounds=None,
attributes=coord.attributes,
coord_system=coord.coord_system)
new_cube.add_aux_coord(new_coord, trajectory_dim)
coord_mapping[id(coord)] = new_coord
for factory in cube.aux_factories:
new_cube.add_aux_factory(factory.updated(coord_mapping))
# Are the given coords all 1-dimensional? (can we do linear interp?)
for coord, values in sample_points:
if coord.ndim > 1:
if method == "linear":
msg = "Cannot currently perform linear interpolation for " \
"multi-dimensional coordinates."
raise iris.exceptions.CoordinateMultiDimError(msg)
method = "nearest"
break
if method in ["linear", None]:
for i in range(trajectory_size):
point = [(coord, values[i]) for coord, values in sample_points]
column = linear_regrid(cube, point)
new_cube.data[..., i] = column.data
# Fill in the empty squashed (non derived) coords.
for column_coord in column.dim_coords + column.aux_coords:
src_dims = cube.coord_dims(column_coord)
if not squish_my_dims.isdisjoint(src_dims):
if len(column_coord.points) != 1:
msg = "Expected to find exactly one point. Found {}."
raise Exception(msg.format(column_coord.points))
new_cube.coord(column_coord.name()).points[i] = \
column_coord.points[0]
elif method == "nearest":
# Use a cache with _nearest_neighbour_indices_ndcoords()
cache = {}
column_indexes = _nearest_neighbour_indices_ndcoords(
cube, sample_points, cache=cache)
# Construct "fancy" indexes, so we can create the result data array in
# a single numpy indexing operation.
# ALSO: capture the index range in each dimension, so that we can fetch
# only a required (square) sub-region of the source data.
fancy_source_indices = []
region_slices = []
n_index_length = len(column_indexes[0])
dims_reduced = [False] * n_index_length
for i_ind in range(n_index_length):
contents = [column_index[i_ind]
for column_index in column_indexes]
each_used = [content != slice(None) for content in contents]
if np.all(each_used):
# This dimension is addressed : use a list of indices.
dims_reduced[i_ind] = True
# Select the region by min+max indices.
start_ind = np.min(contents)
stop_ind = 1 + np.max(contents)
region_slice = slice(start_ind, stop_ind)
# Record point indices with start subtracted from all of them.
fancy_index = list(np.array(contents) - start_ind)
elif not np.any(each_used):
# This dimension is not addressed by the operation.
# Use a ":" as the index.
fancy_index = slice(None)
# No sub-region selection for this dimension.
region_slice = slice(None)
else:
# Should really never happen, if _ndcoords is right.
msg = ('Internal error in trajectory interpolation : point '
'selection indices should all have the same form.')
raise ValueError(msg)
fancy_source_indices.append(fancy_index)
region_slices.append(region_slice)
# Fetch the required (square-section) region of the source data.
# NOTE: This is not quite as good as only fetching the individual
# points used, but it avoids creating a sub-cube for each point,
# which is very slow, especially when points are re-used a lot ...
source_area_indices = tuple(region_slices)
source_data = cube[source_area_indices].data
# Transpose source data before indexing it to get the final result.
# Because.. the fancy indexing will replace the indexed (horizontal)
# dimensions with a new single dimension over trajectory points.
# Move those dimensions to the end *first* : this ensures that the new
# dimension also appears at the end, which is where we want it.
# Make a list of dims with the reduced ones last.
dims_reduced = np.array(dims_reduced)
dims_order = np.arange(n_index_length)
dims_order = np.concatenate((dims_order[~dims_reduced],
dims_order[dims_reduced]))
# Rearrange the data dimensions and the fancy indices into that order.
source_data = source_data.transpose(dims_order)
fancy_source_indices = [fancy_source_indices[i_dim]
for i_dim in dims_order]
# Apply the fancy indexing to get all the result data points.
source_data = source_data[fancy_source_indices]
# "Fix" problems with missing datapoints producing odd values
# when copied from a masked into an unmasked array.
# TODO: proper masked data handling.
if np.ma.isMaskedArray(source_data):
# This is **not** proper mask handling, because we cannot produce a
# masked result, but it ensures we use a "filled" version of the
# input in this case.
source_data = source_data.filled()
new_cube.data[:] = source_data
# NOTE: we assign to "new_cube.data[:]" and *not* just "new_cube.data",
# because the existing code produces a default dtype from 'np.empty'
# instead of preserving the input dtype.
# TODO: maybe this should be fixed -- i.e. to preserve input dtype ??
# Fill in the empty squashed (non derived) coords.
column_coords = [coord
for coord in cube.dim_coords + cube.aux_coords
if not squish_my_dims.isdisjoint(
cube.coord_dims(coord))]
new_cube_coords = [new_cube.coord(column_coord.name())
for column_coord in column_coords]
all_point_indices = np.array(column_indexes)
single_point_test_cube = cube[column_indexes[0]]
for new_cube_coord, src_coord in zip(new_cube_coords, column_coords):
# Check structure of the indexed coord (at one selected point).
point_coord = single_point_test_cube.coord(src_coord)
if len(point_coord.points) != 1:
msg = ('Coord {} at one x-y position has the shape {}, '
'instead of being a single point. ')
raise ValueError(msg.format(src_coord.name(), src_coord.shape))
# Work out which indices apply to the input coord.
# NOTE: we know how to index the source cube to get a cube with a
# single point for each coord, but this is very inefficient.
# So here, we translate cube indexes into *coord* indexes.
src_coord_dims = cube.coord_dims(src_coord)
fancy_coord_index_arrays = [list(all_point_indices[:, src_dim])
for src_dim in src_coord_dims]
# Fill the new coord with all the correct points from the old one.
new_cube_coord.points = src_coord.points[fancy_coord_index_arrays]
# NOTE: the new coords do *not* have bounds.
return new_cube
def interpolate(cube, sample_points, method=None):
"""
Extract a sub-cube at the given n-dimensional points.
Args:
* cube
The source Cube.
* sample_points
A sequence of coordinate (name) - values pairs.
Kwargs:
* method
Request "linear" interpolation (default) or "nearest" neighbour.
Only nearest neighbour is available when specifying multi-dimensional coordinates.
For example::
sample_points = [('latitude', [45, 45, 45]), ('longitude', [-60, -50, -40])]
interpolated_cube = interpolate(cube, sample_points)
"""
if method not in [None, "linear", "nearest"]:
raise ValueError("Unhandled interpolation specified : %s" % method)
# Convert any coordinate names to coords
points = []
for coord, values in sample_points:
if isinstance(coord, six.string_types):
coord = cube.coord(coord)
points.append((coord, values))
sample_points = points
# Do all value sequences have the same number of values?
coord, values = sample_points[0]
trajectory_size = len(values)
for coord, values in sample_points[1:]:
if len(values) != trajectory_size:
raise ValueError('Lengths of coordinate values are inconsistent.')
# Which dimensions are we squishing into the last dimension?
squish_my_dims = set()
for coord, values in sample_points:
dims = cube.coord_dims(coord)
for dim in dims:
squish_my_dims.add(dim)
# Derive the new cube's shape by filtering out all the dimensions we're about to sample,
# and then adding a new dimension to accommodate all the sample points.
remaining = [(dim, size) for dim, size in enumerate(cube.shape) if dim not in squish_my_dims]
new_data_shape = [size for dim, size in remaining]
new_data_shape.append(trajectory_size)
# Start with empty data and then fill in the "column" of values for each trajectory point.
new_cube = iris.cube.Cube(np.empty(new_data_shape))
new_cube.metadata = cube.metadata
# Derive the mapping from the non-trajectory source dimensions to their
# corresponding destination dimensions.
remaining_dims = [dim for dim, size in remaining]
dimension_remap = {dim: i for i, dim in enumerate(remaining_dims)}
# Record a mapping from old coordinate IDs to new coordinates,
# for subsequent use in creating updated aux_factories.
coord_mapping = {}
# Create all the non-squished coords
for coord in cube.dim_coords:
src_dims = cube.coord_dims(coord)
if squish_my_dims.isdisjoint(src_dims):
dest_dims = [dimension_remap[dim] for dim in src_dims]
new_coord = coord.copy()
new_cube.add_dim_coord(new_coord, dest_dims)
coord_mapping[id(coord)] = new_coord
for coord in cube.aux_coords:
src_dims = cube.coord_dims(coord)
if squish_my_dims.isdisjoint(src_dims):
dest_dims = [dimension_remap[dim] for dim in src_dims]
new_coord = coord.copy()
new_cube.add_aux_coord(new_coord, dest_dims)
coord_mapping[id(coord)] = new_coord
# Create all the squished (non derived) coords, not filled in yet.
trajectory_dim = len(remaining_dims)
for coord in cube.dim_coords + cube.aux_coords:
src_dims = cube.coord_dims(coord)
if not squish_my_dims.isdisjoint(src_dims):
points = np.array([coord.points.flatten()[0]] * trajectory_size)
new_coord = iris.coords.AuxCoord(points,
standard_name=coord.standard_name,
long_name=coord.long_name,
units=coord.units,
bounds=None,
attributes=coord.attributes,
coord_system=coord.coord_system)
new_cube.add_aux_coord(new_coord, trajectory_dim)
coord_mapping[id(coord)] = new_coord
for factory in cube.aux_factories:
new_cube.add_aux_factory(factory.updated(coord_mapping))
# Are the given coords all 1-dimensional? (can we do linear interp?)
for coord, values in sample_points:
if coord.ndim > 1:
if method == "linear":
raise iris.exceptions.CoordinateMultiDimError("Cannot currently perform linear interpolation for multi-dimensional coordinates.")
method = "nearest"
break
# Use a cache with _nearest_neighbour_indices_ndcoords()
cache = {}
for i in range(trajectory_size):
point = [(coord, values[i]) for coord, values in sample_points]
if method in ["linear", None]:
column = linear_regrid(cube, point)
new_cube.data[..., i] = column.data
elif method == "nearest":
column_index = _nearest_neighbour_indices_ndcoords(cube, point, cache=cache)
column = cube[column_index]
new_cube.data[..., i] = column.data
# Fill in the empty squashed (non derived) coords.
for column_coord in column.dim_coords + column.aux_coords:
src_dims = cube.coord_dims(column_coord)
if not squish_my_dims.isdisjoint(src_dims):
if len(column_coord.points) != 1:
raise Exception("Expected to find exactly one point. Found %d" % len(column_coord.points))
new_cube.coord(column_coord.name()).points[i] = column_coord.points[0]
return new_cube