def projectField(self, cubes, neofs=None, eofscaling=0, weighted=True):
"""Project a set of fields onto the EOFs.
Given a set of fields, projects them onto the EOFs to generate a
corresponding set of pseudo-PCs.
**Argument:**
*fields*
A list/tuple containing one or more `~iris.cube.Cube`
instances, each with two or more dimensions, containing the
data to be projected onto the EOFs. Each field must have the
same spatial dimensions (including missing values in the
same places) as the corresponding data set in the
`MultivariateEof` input *datasets*. The fields may have
different length time dimensions to the `MultivariateEof`
inputs *datasets* or no time dimension at all, but this
must be consistent for all fields.
**Optional arguments:**
*neofs*
Number of EOFs to project onto. Defaults to all EOFs. If the
number of EOFs requested is more than the number that are
available, then the field will be projected onto all
available EOFs.
*eofscaling*
Set the scaling of the EOFs that are projected
onto. The following values are accepted:
* *0* : Un-scaled EOFs (default).
* *1* : EOFs are divided by the square-root of their
eigenvalue.
* *2* : EOFs are multiplied by the square-root of their
eigenvalue.
*weighted*
If *True* then each field in *fields* is weighted using the
same weights used for the EOF analysis prior to projection.
If *False* then no weighting is applied. Defaults to *True*
(weighting is applied). Generally only the default setting
should be used.
**Returns:**
*pseudo_pcs*
A `~iris.cube.Cube` containing the ordered pseudo-PCs.
**Examples:**
Project a data set onto all EOFs::
pseudo_pcs = solver.projectField([field1, field2])
Project a data set onto the four leading EOFs::
pseudo_pcs = solver.projectField([field1, field2], neofs=4)
"""
for cube in cubes:
if type(cube) is not Cube:
raise TypeError('input is not an iris cube')
if len(cubes) != self._ncubes:
raise ValueError('number of cubes is incorrect, expecting {:d} '
'but got {:d}'.format(self._ncubes, len(cubes)))
for cube in cubes:
try:
# Time dimension must be first.
raise_error = False
time, time_coord = coord_and_dim(cube, 'time')
if time_coord != 0:
raise_error = True
except ValueError:
# Not having a time dimension is also acceptable.
pass
if raise_error:
raise ValueError('time must be the first dimension, '
'consider using the transpose() method')
# Compute the PCs.
pcs = self._solver.projectField([cube.data for cube in cubes],
neofs=neofs,
eofscaling=eofscaling,
weighted=weighted)
# Construct the required dimensions.
if pcs.ndim == 2:
# 2D PCs require a time axis and a PC axis.
pcdim = DimCoord(range(pcs.shape[1]),
var_name='pc',
long_name='pc_number')
time, time_dim = coord_and_dim(cubes[0], 'time')
coords = [time, pcdim]
else:
# 1D PCs require only a PC axis.
pcdim = DimCoord(range(pcs.shape[0]),
var_name='pc',
long_name='pc_number')
coords = [pcdim]
# Construct an Iris cube.
pcs = Cube(pcs,
dim_coords_and_dims=zip(coords, range(pcs.ndim)),
var_name='pseudo_pcs',
long_name='pseudo_pcs')
return pcs
def projectField(self, cubes, neofs=None, eofscaling=0, weighted=True):
"""Project a set of fields onto the EOFs.
Given a set of fields, projects them onto the EOFs to generate a
corresponding set of pseudo-PCs.
**Argument:**
*fields*
A list/tuple containing one or more `~iris.cube.Cube`
instances, each with two or more dimensions, containing the
data to be projected onto the EOFs. Each field must have the
same spatial dimensions (including missing values in the
same places) as the corresponding data set in the
`MultivariateEof` input *datasets*. The fields may have
different length time dimensions to the `MultivariateEof`
inputs *datasets* or no time dimension at all, but this
must be consistent for all fields.
**Optional arguments:**
*neofs*
Number of EOFs to project onto. Defaults to all EOFs. If the
number of EOFs requested is more than the number that are
available, then the field will be projected onto all
available EOFs.
*eofscaling*
Set the scaling of the EOFs that are projected
onto. The following values are accepted:
* *0* : Un-scaled EOFs (default).
* *1* : EOFs are divided by the square-root of their
eigenvalue.
* *2* : EOFs are multiplied by the square-root of their
eigenvalue.
*weighted*
If *True* then each field in *fields* is weighted using the
same weights used for the EOF analysis prior to projection.
If *False* then no weighting is applied. Defaults to *True*
(weighting is applied). Generally only the default setting
should be used.
**Returns:**
*pseudo_pcs*
A `~iris.cube.Cube` containing the ordered pseudo-PCs.
**Examples:**
Project a data set onto all EOFs::
pseudo_pcs = solver.projectField([field1, field2])
Project a data set onto the four leading EOFs::
pseudo_pcs = solver.projectField([field1, field2], neofs=4)
"""
for cube in cubes:
if not isinstance(cube, Cube):
raise TypeError('input is not an iris cube')
if len(cubes) != self._ncubes:
raise ValueError('number of cubes is incorrect, expecting {:d} '
'but got {:d}'.format(self._ncubes, len(cubes)))
_all_time_aux_coords = []
for cube in cubes:
try:
# Time dimension must be first.
raise_error = False
time, time_coord = coord_and_dim(cube, 'time')
if time_coord != 0:
raise_error = True
except ValueError:
# Not having a time dimension is also acceptable.
pass
if raise_error:
raise ValueError('time must be the first dimension, '
'consider using the transpose() method')
# Store any AuxCoords describing the time dimension.
_t, _, _ = classified_aux_coords(cube)
_all_time_aux_coords.append(_t)
# Retain AuxCoords that describe the time dimension of *every* input
# cube.
_common_time_aux_coords = common_items(_all_time_aux_coords)
# Compute the PCs.
pcs = self._solver.projectField([cube.data for cube in cubes],
neofs=neofs,
eofscaling=eofscaling,
weighted=weighted)
pcs = Cube(pcs, var_name='pseudo_pcs', long_name='pseudo_pcs')
# Construct the required dimensions.
if pcs.ndim == 2:
# 2D PCs require a time axis and a PC axis.
pcdim = DimCoord(range(pcs.shape[1]),
var_name='pc',
long_name='pc_number')
time, time_dim = coord_and_dim(cubes[0], 'time')
pcs.add_dim_coord(copy(time), 0)
pcs.add_dim_coord(pcdim, 1)
# Add any auxiliary coordinates for the time dimension.
for coord, dims in _common_time_aux_coords:
pcs.add_aux_coord(copy(coord), dims)
else:
# 1D PCs require only a PC axis.
pcdim = DimCoord(range(pcs.shape[0]),
var_name='pc',
long_name='pc_number')
pcs.add_dim_coord(pcdim, 0)
return pcs
def __init__(self, cubes, weights=None, center=True, ddof=1):
"""Create a MultivariateEof instance.
The EOF solution is computed at initialization time. Method
calls are used to retrieve computed quantities.
**Arguments:**
*cubes*
A list/tuple containing one or more `~iris.cube.Cube`
instances, each with two or more dimensions, containing the
data to be analysed. Time must be the first dimension of
each `~iris.cube.Cube`. Missing values are allowed provided
that they are constant with time in each field (e.g., values
of an oceanographic field over land).
**Optional arguments:**
*weights*
Sets the weighting method. One method can be chosen to apply
to all cubes in *datasets* or a sequence of options can be
given to specify a different weighting method for each cube
in *datasets*. The following pre-defined weighting methods
are available:
* *'area'* : Square-root of grid cell area normalized by
total grid area. Requires a latitude-longitude grid to be
present in the corresponding `~iris.cube.Cube`. This is a
fairly standard weighting strategy. If you are unsure
which method to use and you have gridded data then this
should be your first choice.
* *'coslat'* : Square-root of cosine of latitude. Requires a
latitude dimension to be present in the corresponding
`~iris.cube.Cube`.
* *None* : Equal weights for all grid points (*'none'* is
also accepted).
Alternatively a sequence of arrays of weights whose shapes
are compatible with the corresponding `~iris.cube.Cube`
instances in *datasets* may be supplied instead of
specifying a weighting method.
*center*
If *True*, the mean along the first axis of each cube in
*datasets* (the time-mean) will be removed prior to
analysis. If *False*, the mean along the first axis will not
be removed. Defaults to *True* (mean is removed).
The covariance interpretation relies on the input data being
anomalies with a time-mean of 0. Therefore this option
should usually be set to *True*. Setting this option to
*True* has the useful side effect of propagating missing
values along the time dimension, ensuring that a solution
can be found even if missing values occur in different
locations at different times.
*ddof*
'Delta degrees of freedom'. The divisor used to normalize
the covariance matrix is *N - ddof* where *N* is the
number of samples. Defaults to *1*.
**Returns:**
*solver*
An `MultivariateEof` instance.
**Examples:**
EOF analysis of two cubes with area-weighting::
from eofs.multivariate.iris import MultivariateEof
solver = MultivariateEof(cube1, cube2, weights='area')
"""
# Record the number of input cubes.
self._ncubes = len(cubes)
# Check that the weights argument is valid and refactor it if there
# is only one option provided.
if weights in (None, 'area', 'coslat'):
weights = [weights] * self._ncubes
elif len(weights) != self._ncubes:
raise ValueError('number of weights and cubes must match')
# Process each input cube recording its time dimension coordinate,
# other dimension coordinates, and defining its weight array.
self._time = []
self._coords = []
passweights = []
for cube, weight in zip(cubes, weights):
if type(cube) is not Cube:
raise TypeError('input is not an iris cube')
# Record the time dimension and it's position. If its position is
# not 0 then raise an error.
time, time_dim = coord_and_dim(cube, 'time')
if time_dim != 0:
raise ValueError('time must be the first dimension, '
'consider using the transpose() method')
self._time.append(time)
# Make a list of the cube's other dimension coordinates.
coords = list(copy(cube.dim_coords))
coords.remove(time)
if len(coords) < 1:
raise ValueError('one or more non-time '
'dimensions are required')
self._coords.append(coords)
# Determine the weighting option for the cube.
if weight is None:
wtarray = None
else:
try:
scheme = weight.lower()
wtarray = weights_array(cube, scheme=scheme)
except AttributeError:
wtarray = weight
try:
wtarray = wtarray.astype(cube.data.dtype)
except AttributeError:
pass
passweights.append(wtarray)
# Create a solver.
self._solver = standard.MultivariateEof(
[cube.data for cube in cubes],
weights=passweights,
center=center,
ddof=ddof)
#: Number of EOFs in the solution.
self.neofs = self._solver.neofs
# Names of the cubes.
self._cube_names = map(
lambda c: c.name(default='dataset').replace(' ', '_'), cubes)
self._cube_var_names = [cube.var_name for cube in cubes]
def __init__(self, cubes, weights=None, center=True, ddof=1):
"""Create a MultivariateEof instance.
The EOF solution is computed at initialization time. Method
calls are used to retrieve computed quantities.
**Arguments:**
*cubes*
A list/tuple containing one or more `~iris.cube.Cube`
instances, each with two or more dimensions, containing the
data to be analysed. Time must be the first dimension of
each `~iris.cube.Cube`. Missing values are allowed provided
that they are constant with time in each field (e.g., values
of an oceanographic field over land).
**Optional arguments:**
*weights*
Sets the weighting method. One method can be chosen to apply
to all cubes in *datasets* or a sequence of options can be
given to specify a different weighting method for each cube
in *datasets*. The following pre-defined weighting methods
are available:
* *'area'* : Square-root of grid cell area normalized by
total grid area. Requires a latitude-longitude grid to be
present in the corresponding `~iris.cube.Cube`. This is a
fairly standard weighting strategy. If you are unsure
which method to use and you have gridded data then this
should be your first choice.
* *'coslat'* : Square-root of cosine of latitude. Requires a
latitude dimension to be present in the corresponding
`~iris.cube.Cube`.
* *None* : Equal weights for all grid points (*'none'* is
also accepted).
Alternatively a sequence of arrays of weights whose shapes
are compatible with the corresponding `~iris.cube.Cube`
instances in *datasets* may be supplied instead of
specifying a weighting method.
*center*
If *True*, the mean along the first axis of each cube in
*datasets* (the time-mean) will be removed prior to
analysis. If *False*, the mean along the first axis will not
be removed. Defaults to *True* (mean is removed).
The covariance interpretation relies on the input data being
anomalies with a time-mean of 0. Therefore this option
should usually be set to *True*. Setting this option to
*True* has the useful side effect of propagating missing
values along the time dimension, ensuring that a solution
can be found even if missing values occur in different
locations at different times.
*ddof*
'Delta degrees of freedom'. The divisor used to normalize
the covariance matrix is *N - ddof* where *N* is the
Reconstruct the input field using EOFs 1, 2 and 5::
reconstruction = solver.reconstuctedField([1, 2, 5])
number of samples. Defaults to *1*.
**Returns:**
*solver*
An `MultivariateEof` instance.
**Examples:**
EOF analysis of two cubes with area-weighting::
from eofs.multivariate.iris import MultivariateEof
solver = MultivariateEof(cube1, cube2, weights='area')
"""
# Record the number of input cubes.
self._ncubes = len(cubes)
# Check that the weights argument is valid and refactor it if there
# is only one option provided.
if weights in (None, 'area', 'coslat'):
weights = [weights] * self._ncubes
elif len(weights) != self._ncubes:
raise ValueError('number of weights and cubes must match')
# Process each input cube recording its time dimension coordinate,
# other dimension coordinates, and defining its weight array.
self._time = []
self._coords = []
self._time_aux_coords = []
self._space_aux_coords = []
self._time_space_aux_coords = []
passweights = []
for cube, weight in zip(cubes, weights):
if not isinstance(cube, Cube):
raise TypeError('input is not an iris cube')
# Record the time dimension and it's position. If its position is
# not 0 then raise an error.
time, time_dim = coord_and_dim(cube, 'time')
if time_dim != 0:
raise ValueError('time must be the first dimension, '
'consider using the transpose() method')
self._time.append(copy(time))
# Make a list of the cube's other dimension coordinates.
coords = [copy(coord) for coord in cube.dim_coords]
coords.remove(time)
if not coords:
raise ValueError('one or more non-time '
'dimensions are required')
self._coords.append(coords)
# Make a lists of the AuxCoords on the current cube and store
# them for reapplication later.
_t, _s, _ts = classified_aux_coords(cube)
self._time_aux_coords.append(_t)
self._space_aux_coords.append(_s)
self._time_space_aux_coords.append(_ts)
# Determine the weighting option for the cube.
if weight is None:
wtarray = None
else:
try:
scheme = weight.lower()
wtarray = weights_array(cube, scheme=scheme)
except AttributeError:
wtarray = weight
try:
wtarray = wtarray.astype(cube.data.dtype)
except AttributeError:
pass
passweights.append(wtarray)
# Get a list of all the auxiliary coordinates that span just time
# and are present on every input cube.
self._common_time_aux_coords = common_items(self._time_aux_coords)
# Create a solver.
self._solver = standard.MultivariateEof([cube.data for cube in cubes],
weights=passweights,
center=center,
ddof=ddof)
#: Number of EOFs in the solution.
self.neofs = self._solver.neofs
# Names of the cubes.
self._cube_names = map(
lambda c: c.name(default='dataset').replace(' ', '_'), cubes)
self._cube_var_names = [cube.var_name for cube in cubes]