def __init__(self, *datasets, **kwargs):
"""Create a MultipleEofSolver object.
The EOF solution is computed at initialization time. Method
calls are used to retrieve computed quantities.
**Arguments:**
*\*datasets*
One or more :py:class:`numpy.ndarray`s or
:py:class:`numpy.ma.core.MasekdArray`s with two or more
dimensions containing the data to be analysed. The first
dimension of each array is assumed to represent time.
Missing values are permitted, either in the form of masked
arrays, or the value :py:attr:`numpy.nan`. Missing values
must be constant with time (e.g., values of an oceanographic
field over land).
**Optional arguments:**
*weights*
A sequence of arrays of weights whose shapes are compatible
with those of the input data sets. The weights can have the
same shape as the input data set or a shape compatible with
a an array broadcast operation (ie. the shape of the weights
can match the rightmost parts of the shape of the input data
set). If none of the input data sets require weighting then
the single value *None* may be used. Defaults to *None* (no
weighting for any data set).
*center*
If *True*, the mean along the first axis of the input data
set (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). Generally this option
should be set to *True* as the covariance interpretation
relies on input data being anomalies with a time-mean of 0.
A valid reson for turning this off would be if you have
already generated an anomaly data set. Setting to *True* has
the useful side-effect of propagating missing values along
the time-dimension, ensuring the solver will work even if
missing values occur at 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*.
"""
# Define valid keyword arguments and their default values. This method
# is required since Python 2.7 cannot accept a variable argument list
# followed by a set of keyword arguments. For some reason both must be
# variable.
keywords = {"weights": None, "center": True, "ddof": 1}
for kwarg in kwargs.keys():
if kwarg not in keywords.keys():
raise EofError("invalid argument: %s" % kwarg)
weights = kwargs.get("weights", keywords["weights"])
center = kwargs.get("center", keywords["center"])
ddof = kwargs.get("ddof", keywords["ddof"])
# Record the number of datasets provided.
self._ndatasets = len(datasets)
# Initialise instance variables dealing with dataset shapes.
self._multirecords = list()
self._multishapes = list()
self._multislicers = list()
self._multichannels = list()
self._multidtypes = list()
slicebegin = 0
for dataset in datasets:
records = dataset.shape[0]
shape = dataset.shape[1:]
channels = np.product(shape)
slicer = slice(slicebegin, slicebegin+channels)
slicebegin += channels
self._multirecords.append(records)
self._multishapes.append(shape)
self._multislicers.append(slicer)
self._multichannels.append(channels)
self._multidtypes.append(dataset.dtype)
# Check that all fields have the same time dimension.
if not (np.array(self._multirecords) == self._multirecords[0]).all():
raise EofError("all datasets must have the same first dimension")
# Get the dtype that will be used for the data and weights. This will
# be the 'highest' dtype of those passed.
dtype = sorted(self._multidtypes, reverse=True)[0]
# Form a full array to pass to the EOF solver consisting of all the
# flat inputs.
nt = self._multirecords[0]
ns = self._multichannels.sum()
dataset = ma.empty([nt, ns], dtype=dtype)
for iset in xrange(self._ndatasets):
slicer = self._multislicers[iset]
channels = self._multichannels[iset]
dataset[:, slicer] = datasets[iset].reshape([nt, channels])
# Construct an array of weights the same shape as the data array.
if weights is not None:
if len(weights) != self._ndatasets:
raise EofError("number of weights and datasets differs")
if not filter(lambda i: False if i is None else True, weights):
# If every entry in the weights list is None then just pass
# None to the EofSolver __init__ method.
warr = None
else:
# Construct a spatial weights array.
warr = np.empty([1, ns], dtype=dtype)
for iset in xrange(self._ndatasets):
slicer = self._multislicers[iset]
if weights[iset] is None:
# If this dataset has no weights use 1 for the weight
# of all elements.
warr[:, slicer] = 1.
else:
# Otherwise use the weights. These need to be
# conformed to the correct dimensions.
channels = self._multichannels[iset]
try:
warr[:, slicer] = np.broadcast_arrays(
datasets[iset][0],
weights[iset])[1].reshape([channels])
except ValueError:
raise EofError("weights are invalid")
else:
# Just pass None if none of the input datasets have associated
# weights.
warr = None
# Create an EofSolver object to handle the computations.
self._solver = EofSolver(dataset, weights=warr, center=center, ddof=1)
class MultipleEofSolver(object):
"""Multiple EOF analysis (:py:mod:`numpy` interface)."""
def __init__(self, *datasets, **kwargs):
"""Create a MultipleEofSolver object.
The EOF solution is computed at initialization time. Method
calls are used to retrieve computed quantities.
**Arguments:**
*\*datasets*
One or more :py:class:`numpy.ndarray`s or
:py:class:`numpy.ma.core.MasekdArray`s with two or more
dimensions containing the data to be analysed. The first
dimension of each array is assumed to represent time.
Missing values are permitted, either in the form of masked
arrays, or the value :py:attr:`numpy.nan`. Missing values
must be constant with time (e.g., values of an oceanographic
field over land).
**Optional arguments:**
*weights*
A sequence of arrays of weights whose shapes are compatible
with those of the input data sets. The weights can have the
same shape as the input data set or a shape compatible with
a an array broadcast operation (ie. the shape of the weights
can match the rightmost parts of the shape of the input data
set). If none of the input data sets require weighting then
the single value *None* may be used. Defaults to *None* (no
weighting for any data set).
*center*
If *True*, the mean along the first axis of the input data
set (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). Generally this option
should be set to *True* as the covariance interpretation
relies on input data being anomalies with a time-mean of 0.
A valid reson for turning this off would be if you have
already generated an anomaly data set. Setting to *True* has
the useful side-effect of propagating missing values along
the time-dimension, ensuring the solver will work even if
missing values occur at 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*.
"""
# Define valid keyword arguments and their default values. This method
# is required since Python 2.7 cannot accept a variable argument list
# followed by a set of keyword arguments. For some reason both must be
# variable.
keywords = {"weights": None, "center": True, "ddof": 1}
for kwarg in kwargs.keys():
if kwarg not in keywords.keys():
raise EofError("invalid argument: %s" % kwarg)
weights = kwargs.get("weights", keywords["weights"])
center = kwargs.get("center", keywords["center"])
ddof = kwargs.get("ddof", keywords["ddof"])
# Record the number of datasets provided.
self._ndatasets = len(datasets)
# Initialise instance variables dealing with dataset shapes.
self._multirecords = list()
self._multishapes = list()
self._multislicers = list()
self._multichannels = list()
self._multidtypes = list()
slicebegin = 0
for dataset in datasets:
records = dataset.shape[0]
shape = dataset.shape[1:]
channels = np.product(shape)
slicer = slice(slicebegin, slicebegin+channels)
slicebegin += channels
self._multirecords.append(records)
self._multishapes.append(shape)
self._multislicers.append(slicer)
self._multichannels.append(channels)
self._multidtypes.append(dataset.dtype)
# Check that all fields have the same time dimension.
if not (np.array(self._multirecords) == self._multirecords[0]).all():
raise EofError("all datasets must have the same first dimension")
# Get the dtype that will be used for the data and weights. This will
# be the 'highest' dtype of those passed.
dtype = sorted(self._multidtypes, reverse=True)[0]
# Form a full array to pass to the EOF solver consisting of all the
# flat inputs.
nt = self._multirecords[0]
ns = self._multichannels.sum()
dataset = ma.empty([nt, ns], dtype=dtype)
for iset in xrange(self._ndatasets):
slicer = self._multislicers[iset]
channels = self._multichannels[iset]
dataset[:, slicer] = datasets[iset].reshape([nt, channels])
# Construct an array of weights the same shape as the data array.
if weights is not None:
if len(weights) != self._ndatasets:
raise EofError("number of weights and datasets differs")
if not filter(lambda i: False if i is None else True, weights):
# If every entry in the weights list is None then just pass
# None to the EofSolver __init__ method.
warr = None
else:
# Construct a spatial weights array.
warr = np.empty([1, ns], dtype=dtype)
for iset in xrange(self._ndatasets):
slicer = self._multislicers[iset]
if weights[iset] is None:
# If this dataset has no weights use 1 for the weight
# of all elements.
warr[:, slicer] = 1.
else:
# Otherwise use the weights. These need to be
# conformed to the correct dimensions.
channels = self._multichannels[iset]
try:
warr[:, slicer] = np.broadcast_arrays(
datasets[iset][0],
weights[iset])[1].reshape([channels])
except ValueError:
raise EofError("weights are invalid")
else:
# Just pass None if none of the input datasets have associated
# weights.
warr = None
# Create an EofSolver object to handle the computations.
self._solver = EofSolver(dataset, weights=warr, center=center, ddof=1)
def _unwrap(self, modes):
"""Split a returned mode field into component parts."""
nmodes = modes.shape[0]
modeset = [modes[:, slicer].reshape((nmodes,)+shape) \
for slicer, shape in zip(self._multislicers, self._multishapes)]
return modeset
def pcs(self, pcscaling=0, npcs=None):
"""Principal component time series (PCs).
Returns an array where the columns are the ordered PCs.
**Optional arguments:**
*pcscaling*
Set the scaling of the retrieved PCs. The following
values are accepted:
* *0* : Un-scaled PCs (default).
* *1* : PCs are scaled to unit variance (divided by the
square-root of their eigenvalue).
* *2* : PCs are multiplied by the square-root of their
eigenvalue.
*npcs* : Number of PCs to retrieve. Defaults to all the PCs.
"""
return self._solver.pcs(pcscaling, npcs)
def eofs(self, eofscaling=0, neofs=None):
"""Empirical orthogonal functions (EOFs).
Returns arrays with the ordered EOFs along the first
dimension.
**Optional arguments:**
*eofscaling*
Sets the scaling of the EOFs. The following values are
accepted:
* *0* : Un-scaled EOFs (default).
* *1* : EOFs are divided by the square-root of their
eigenvalues.
* *2* : EOFs are multiplied by the square-root of their
eigenvalues.
*neofs* -- Number of EOFs to return. Defaults to all EOFs.
"""
modes = self._solver.eofs(eofscaling, neofs)
return self._unwrap(modes)
def eigenvalues(self, neigs=None):
"""Eigenvalues (decreasing variances) associated with each EOF.
**Optional argument:**
*neigs*
Number of eigenvalues to return. Defaults to all
eigenvalues.
"""
return self._solver.eigenvalues(neigs)
def eofsAsCorrelation(self, neofs=None):
"""
EOFs scaled as the correlation of the PCs with the original
field.
**Optional argument:**
*neofs*
Number of EOFs to return. Defaults to all EOFs.
"""
modes = self._solver.eofsAsCorrelation(neofs)
return self._unwrap(modes)
def eofsAsCovariance(self, neofs=None, pcscaling=1):
"""
EOFs scaled as the covariance of the PCs with the original
field.
**Optional arguments:**
*neofs*
Number of EOFs to return. Defaults to all EOFs.
*pcscaling*
Set the scaling of the PCs used to compute covariance. The
following values are accepted:
* *0* : Un-scaled PCs.
* *1* : PCs are scaled to unit variance (divided by the
square-root of their eigenvalue) (default).
* *2* : PCs are multiplied by the square-root of their
eigenvalue.
"""
modes = self._solver.eofsAsCovariance(neofs, pcscaling)
return self._unwrap(modes)
def varianceFraction(self, neigs=None):
"""Fractional EOF variances.
The fraction of the total variance explained by each EOF. This
is a value between 0 and 1 inclusive.
**Optional argument:**
*neigs*
Number of eigenvalues to return the fractional variance for.
Defaults to all eigenvalues.
"""
return self._solver.varianceFraction(neigs)
def totalAnomalyVariance(self):
"""
Total variance associated with the field of anomalies (the sum
of the eigenvalues).
"""
return self._solver.totalAnomalyVariance()
def reconstructedField(self, neofs):
"""Reconstructed data field based on a subset of EOFs.
If weights were passed to the
:py:class:`~eof2.MultipleEofSolver` instance then the returned
reconstructed field will be automatically un-weighted. Otherwise
the returned reconstructed field will be weighted in the same
manner as the input to the
:py:class:`~eof2.MultipleEofSolver` instance.
**Argument:**
*neofs*
Number of EOFs to use for the reconstruction.
"""
rf = self._solver.reconstructedField(neofs)
return self._unwrap(rf)
def northTest(self, neigs=None, vfscaled=False):
"""Typical errors for eigenvalues.
The method of North et al. (1982) is used to compute the typical
error for each eigenvalue. It is assumed that the number of
times in the input data set is the same as the number of
independent realizations. If this assumption is not valid then
the result may be inappropriate.
**Optional arguments:**
*neigs*
The number of eigenvalues to return typical errors for.
Defaults to typical errors for all eigenvalues.
*vfscaled*
If *True* scale the errors by the sum of the eigenvalues.
This yields typical errors with the same scale as the
values returned by the
:py:meth:`~eof2.MultipleEofSolver.varianceFraction`
method. If *False* then no scaling is done. Defaults to
*False* (no scaling).
**References**
North, G. R., T. L. Bell, R. F. Cahalan, and F. J. Moeng, 1982:
"Sampling errors in the estimation of empirical orthogonal
functions", *Monthly Weather Review*, **110**, pages 669-706.
"""
return self._solver.northTest(neigs, vfscaled)
def getWeights(self):
"""Weights used for the analysis."""
w = self._solver.getWeights()
return self._unwrap(w)
def projectField(self, *fields, **kwargs):
"""Project a set of fields onto the EOFs.
Given a set of fields, projects them onto the EOFs to generate
a corresponding set of time series. Fields can be projected onto
all the EOFs or just a subset. There must be the same number of
fields as were originally input into the
:py:class:`~eof2.MultipleEofSolver` instance, and each field
must have the same corresponding spatial dimensions (including
missing values in the same places). The fields may have a
different length time dimension to the original input fields (or
no time dimension at all).
**Argument:**
*\*fields*
One or more fields to project onto the EOFs. The number of
fields must be the same as the number of fields used to
initialize the :py:class:`~eof2.MultipleEofSolver`
instance.
**Optional arguments:**
*missing*
The missing value for all fields, or a list of the
missing value for each field. If not supplied no particular
value is assumed to be missing. Note that if
:py:attr:`numpy.nan` is used to represent missing values
then this option does not need to be used as this case is
handled automatically by the solver.
*neofs*
Number of EOFs to project onto. Defaults to all 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 the EOFs are weighted prior to projection. If
*False* then no weighting is applied. Defaults to *True*
(weighting is applied). Generally only the default setting
should be used.
*notime*
If *True*, indicates that the input fields have no time
dimension and should be treated as spatial data. If *False*
then the first dimension of each input field will be assumed
to be a time dimension. Defaults to *False* (a time
dimension is assumed).
"""
if len(fields) != self._ndatasets:
raise EofError("number of fields differ from original input")
# Handle keyword arguments manually. This works around an issue in
# Python where defined keyword arguments cannot follow a variable
# length regular argument list.
keywords = {"neofs": None, "eofscaling": 0, "weighted": True,
"notime": False}
for kwarg in kwargs.keys():
if kwarg not in keywords.keys():
raise EofEorror("invalid argument: %s" % kwarg)
neofs = kwargs.get("neofs", keywords["neofs"])
eofscaling = kwargs.get("eofscaling", keywords["eofscaling"])
weighted = kwargs.get("weighted", keywords["weighted"])
notime = kwargs.get("notime", keywords["notime"])
# Record shape information about the input fields.
multirecords = list()
multichannels = list()
multidtypes = list()
for iset, field in enumerate(fields):
if notime:
records = 0
shape = field.shape
else:
records = field.shape[0]
shape = field.shape[1:]
channels = np.product(shape)
if channels != self._multichannels[iset]:
raise EofError("spatial dimensions do not match original fields")
multirecords.append(records)
multichannels.append(channels)
multidtypes.append(field.dtype)
# Check that all fields have the same time dimension.
if not (np.array(multirecords) == multirecords[0]).all():
raise EofError("all datasets must have the same first dimension")
# Get the dtype that will be used for the data. This will be the
# 'highest' dtype of those passed.
dtype = sorted(multidtypes, reverse=True)[0]
# Form a full array to pass to the EOF solver consisting of all the
# combined flat inputs.
nt = multirecords[0]
ns = self._multichannels.sum()
outdims = filter(None, [nt, ns])
cfields = ma.empty(outdims, dtype=dtype)
for iset in xrange(self._ndatasets):
slicer = self._multislicers[iset]
channels = self._multichannels[iset]
dims = filter(None, [nt, channels])
cfields[..., slicer] = fields[iset].reshape(dims)
# Compute the projection using the EofSolver object.
pcs = self._solver.projectField(cfields, neofs=neofs,
eofscaling=eofscaling, weighted=weighted, notime=notime)
return pcs
class MultipleEofSolver(object):
"""Multiple EOF analysis (:py:mod:`numpy` interface)."""
def __init__(self, *datasets, **kwargs):
"""Create a MultipleEofSolver object.
The EOF solution is computed at initialization time. Method
calls are used to retrieve computed quantities.
**Arguments:**
*\*datasets*
One or more :py:class:`numpy.ndarray`s or
:py:class:`numpy.ma.core.MasekdArray`s with two or more
dimensions containing the data to be analysed. The first
dimension of each array is assumed to represent time.
Missing values are permitted, either in the form of masked
arrays, or the value :py:attr:`numpy.nan`. Missing values
must be constant with time (e.g., values of an oceanographic
field over land).
**Optional arguments:**
*weights*
A sequence of arrays of weights whose shapes are compatible
with those of the input data sets. The weights can have the
same shape as the input data set or a shape compatible with
a an array broadcast operation (ie. the shape of the weights
can match the rightmost parts of the shape of the input data
set). If none of the input data sets require weighting then
the single value *None* may be used. Defaults to *None* (no
weighting for any data set).
*center*
If *True*, the mean along the first axis of the input data
set (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). Generally this option
should be set to *True* as the covariance interpretation
relies on input data being anomalies with a time-mean of 0.
A valid reson for turning this off would be if you have
already generated an anomaly data set. Setting to *True* has
the useful side-effect of propagating missing values along
the time-dimension, ensuring the solver will work even if
missing values occur at 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*.
"""
# Define valid keyword arguments and their default values. This method
# is required since Python 2.7 cannot accept a variable argument list
# followed by a set of keyword arguments. For some reason both must be
# variable.
keywords = {"weights": None, "center": True, "ddof": 1}
for kwarg in kwargs.keys():
if kwarg not in keywords.keys():
raise EofError("invalid argument: %s" % kwarg)
weights = kwargs.get("weights", keywords["weights"])
center = kwargs.get("center", keywords["center"])
ddof = kwargs.get("ddof", keywords["ddof"])
# Record the number of datasets provided.
self._ndatasets = len(datasets)
# Initialise instance variables dealing with dataset shapes.
self._multirecords = list()
self._multishapes = list()
self._multislicers = list()
self._multichannels = list()
self._multidtypes = list()
slicebegin = 0
for dataset in datasets:
records = dataset.shape[0]
shape = dataset.shape[1:]
channels = np.product(shape)
slicer = slice(slicebegin, slicebegin + channels)
slicebegin += channels
self._multirecords.append(records)
self._multishapes.append(shape)
self._multislicers.append(slicer)
self._multichannels.append(channels)
self._multidtypes.append(dataset.dtype)
# Check that all fields have the same time dimension.
if not (np.array(self._multirecords) == self._multirecords[0]).all():
raise EofError("all datasets must have the same first dimension")
# Get the dtype that will be used for the data and weights. This will
# be the 'highest' dtype of those passed.
dtype = sorted(self._multidtypes, reverse=True)[0]
# Form a full array to pass to the EOF solver consisting of all the
# flat inputs.
nt = self._multirecords[0]
ns = self._multichannels.sum()
dataset = ma.empty([nt, ns], dtype=dtype)
for iset in xrange(self._ndatasets):
slicer = self._multislicers[iset]
channels = self._multichannels[iset]
dataset[:, slicer] = datasets[iset].reshape([nt, channels])
# Construct an array of weights the same shape as the data array.
if weights is not None:
if len(weights) != self._ndatasets:
raise EofError("number of weights and datasets differs")
if not filter(lambda i: False if i is None else True, weights):
# If every entry in the weights list is None then just pass
# None to the EofSolver __init__ method.
warr = None
else:
# Construct a spatial weights array.
warr = np.empty([1, ns], dtype=dtype)
for iset in xrange(self._ndatasets):
slicer = self._multislicers[iset]
if weights[iset] is None:
# If this dataset has no weights use 1 for the weight
# of all elements.
warr[:, slicer] = 1.
else:
# Otherwise use the weights. These need to be
# conformed to the correct dimensions.
channels = self._multichannels[iset]
try:
warr[:, slicer] = np.broadcast_arrays(
datasets[iset][0],
weights[iset])[1].reshape([channels])
except ValueError:
raise EofError("weights are invalid")
else:
# Just pass None if none of the input datasets have associated
# weights.
warr = None
# Create an EofSolver object to handle the computations.
self._solver = EofSolver(dataset, weights=warr, center=center, ddof=1)
def _unwrap(self, modes):
"""Split a returned mode field into component parts."""
nmodes = modes.shape[0]
modeset = [modes[:, slicer].reshape((nmodes,)+shape) \
for slicer, shape in zip(self._multislicers, self._multishapes)]
return modeset
def pcs(self, pcscaling=0, npcs=None):
"""Principal component time series (PCs).
Returns an array where the columns are the ordered PCs.
**Optional arguments:**
*pcscaling*
Set the scaling of the retrieved PCs. The following
values are accepted:
* *0* : Un-scaled PCs (default).
* *1* : PCs are scaled to unit variance (divided by the
square-root of their eigenvalue).
* *2* : PCs are multiplied by the square-root of their
eigenvalue.
*npcs* : Number of PCs to retrieve. Defaults to all the PCs.
"""
return self._solver.pcs(pcscaling, npcs)
def eofs(self, eofscaling=0, neofs=None):
"""Empirical orthogonal functions (EOFs).
Returns arrays with the ordered EOFs along the first
dimension.
**Optional arguments:**
*eofscaling*
Sets the scaling of the EOFs. The following values are
accepted:
* *0* : Un-scaled EOFs (default).
* *1* : EOFs are divided by the square-root of their
eigenvalues.
* *2* : EOFs are multiplied by the square-root of their
eigenvalues.
*neofs* -- Number of EOFs to return. Defaults to all EOFs.
"""
modes = self._solver.eofs(eofscaling, neofs)
return self._unwrap(modes)
def eigenvalues(self, neigs=None):
"""Eigenvalues (decreasing variances) associated with each EOF.
**Optional argument:**
*neigs*
Number of eigenvalues to return. Defaults to all
eigenvalues.
"""
return self._solver.eigenvalues(neigs)
def eofsAsCorrelation(self, neofs=None):
"""
EOFs scaled as the correlation of the PCs with the original
field.
**Optional argument:**
*neofs*
Number of EOFs to return. Defaults to all EOFs.
"""
modes = self._solver.eofsAsCorrelation(neofs)
return self._unwrap(modes)
def eofsAsCovariance(self, neofs=None, pcscaling=1):
"""
EOFs scaled as the covariance of the PCs with the original
field.
**Optional arguments:**
*neofs*
Number of EOFs to return. Defaults to all EOFs.
*pcscaling*
Set the scaling of the PCs used to compute covariance. The
following values are accepted:
* *0* : Un-scaled PCs.
* *1* : PCs are scaled to unit variance (divided by the
square-root of their eigenvalue) (default).
* *2* : PCs are multiplied by the square-root of their
eigenvalue.
"""
modes = self._solver.eofsAsCovariance(neofs, pcscaling)
return self._unwrap(modes)
def varianceFraction(self, neigs=None):
"""Fractional EOF variances.
The fraction of the total variance explained by each EOF. This
is a value between 0 and 1 inclusive.
**Optional argument:**
*neigs*
Number of eigenvalues to return the fractional variance for.
Defaults to all eigenvalues.
"""
return self._solver.varianceFraction(neigs)
def totalAnomalyVariance(self):
"""
Total variance associated with the field of anomalies (the sum
of the eigenvalues).
"""
return self._solver.totalAnomalyVariance()
def reconstructedField(self, neofs):
"""Reconstructed data field based on a subset of EOFs.
If weights were passed to the
:py:class:`~eof2.MultipleEofSolver` instance then the returned
reconstructed field will be automatically un-weighted. Otherwise
the returned reconstructed field will be weighted in the same
manner as the input to the
:py:class:`~eof2.MultipleEofSolver` instance.
**Argument:**
*neofs*
Number of EOFs to use for the reconstruction.
"""
rf = self._solver.reconstructedField(neofs)
return self._unwrap(rf)
def northTest(self, neigs=None, vfscaled=False):
"""Typical errors for eigenvalues.
The method of North et al. (1982) is used to compute the typical
error for each eigenvalue. It is assumed that the number of
times in the input data set is the same as the number of
independent realizations. If this assumption is not valid then
the result may be inappropriate.
**Optional arguments:**
*neigs*
The number of eigenvalues to return typical errors for.
Defaults to typical errors for all eigenvalues.
*vfscaled*
If *True* scale the errors by the sum of the eigenvalues.
This yields typical errors with the same scale as the
values returned by the
:py:meth:`~eof2.MultipleEofSolver.varianceFraction`
method. If *False* then no scaling is done. Defaults to
*False* (no scaling).
**References**
North, G. R., T. L. Bell, R. F. Cahalan, and F. J. Moeng, 1982:
"Sampling errors in the estimation of empirical orthogonal
functions", *Monthly Weather Review*, **110**, pages 669-706.
"""
return self._solver.northTest(neigs, vfscaled)
def getWeights(self):
"""Weights used for the analysis."""
w = self._solver.getWeights()
return self._unwrap(w)
def projectField(self, *fields, **kwargs):
"""Project a set of fields onto the EOFs.
Given a set of fields, projects them onto the EOFs to generate
a corresponding set of time series. Fields can be projected onto
all the EOFs or just a subset. There must be the same number of
fields as were originally input into the
:py:class:`~eof2.MultipleEofSolver` instance, and each field
must have the same corresponding spatial dimensions (including
missing values in the same places). The fields may have a
different length time dimension to the original input fields (or
no time dimension at all).
**Argument:**
*\*fields*
One or more fields to project onto the EOFs. The number of
fields must be the same as the number of fields used to
initialize the :py:class:`~eof2.MultipleEofSolver`
instance.
**Optional arguments:**
*missing*
The missing value for all fields, or a list of the
missing value for each field. If not supplied no particular
value is assumed to be missing. Note that if
:py:attr:`numpy.nan` is used to represent missing values
then this option does not need to be used as this case is
handled automatically by the solver.
*neofs*
Number of EOFs to project onto. Defaults to all 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 the EOFs are weighted prior to projection. If
*False* then no weighting is applied. Defaults to *True*
(weighting is applied). Generally only the default setting
should be used.
*notime*
If *True*, indicates that the input fields have no time
dimension and should be treated as spatial data. If *False*
then the first dimension of each input field will be assumed
to be a time dimension. Defaults to *False* (a time
dimension is assumed).
"""
if len(fields) != self._ndatasets:
raise EofError("number of fields differ from original input")
# Handle keyword arguments manually. This works around an issue in
# Python where defined keyword arguments cannot follow a variable
# length regular argument list.
keywords = {
"neofs": None,
"eofscaling": 0,
"weighted": True,
"notime": False
}
for kwarg in kwargs.keys():
if kwarg not in keywords.keys():
raise EofEorror("invalid argument: %s" % kwarg)
neofs = kwargs.get("neofs", keywords["neofs"])
eofscaling = kwargs.get("eofscaling", keywords["eofscaling"])
weighted = kwargs.get("weighted", keywords["weighted"])
notime = kwargs.get("notime", keywords["notime"])
# Record shape information about the input fields.
multirecords = list()
multichannels = list()
multidtypes = list()
for iset, field in enumerate(fields):
if notime:
records = 0
shape = field.shape
else:
records = field.shape[0]
shape = field.shape[1:]
channels = np.product(shape)
if channels != self._multichannels[iset]:
raise EofError(
"spatial dimensions do not match original fields")
multirecords.append(records)
multichannels.append(channels)
multidtypes.append(field.dtype)
# Check that all fields have the same time dimension.
if not (np.array(multirecords) == multirecords[0]).all():
raise EofError("all datasets must have the same first dimension")
# Get the dtype that will be used for the data. This will be the
# 'highest' dtype of those passed.
dtype = sorted(multidtypes, reverse=True)[0]
# Form a full array to pass to the EOF solver consisting of all the
# combined flat inputs.
nt = multirecords[0]
ns = self._multichannels.sum()
outdims = filter(None, [nt, ns])
cfields = ma.empty(outdims, dtype=dtype)
for iset in xrange(self._ndatasets):
slicer = self._multislicers[iset]
channels = self._multichannels[iset]
dims = filter(None, [nt, channels])
cfields[..., slicer] = fields[iset].reshape(dims)
# Compute the projection using the EofSolver object.
pcs = self._solver.projectField(cfields,
neofs=neofs,
eofscaling=eofscaling,
weighted=weighted,
notime=notime)
return pcs
def __init__(self, *datasets, **kwargs):
"""Create a MultipleEofSolver object.
The EOF solution is computed at initialization time. Method
calls are used to retrieve computed quantities.
**Arguments:**
*\*datasets*
One or more :py:class:`numpy.ndarray`s or
:py:class:`numpy.ma.core.MasekdArray`s with two or more
dimensions containing the data to be analysed. The first
dimension of each array is assumed to represent time.
Missing values are permitted, either in the form of masked
arrays, or the value :py:attr:`numpy.nan`. Missing values
must be constant with time (e.g., values of an oceanographic
field over land).
**Optional arguments:**
*weights*
A sequence of arrays of weights whose shapes are compatible
with those of the input data sets. The weights can have the
same shape as the input data set or a shape compatible with
a an array broadcast operation (ie. the shape of the weights
can match the rightmost parts of the shape of the input data
set). If none of the input data sets require weighting then
the single value *None* may be used. Defaults to *None* (no
weighting for any data set).
*center*
If *True*, the mean along the first axis of the input data
set (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). Generally this option
should be set to *True* as the covariance interpretation
relies on input data being anomalies with a time-mean of 0.
A valid reson for turning this off would be if you have
already generated an anomaly data set. Setting to *True* has
the useful side-effect of propagating missing values along
the time-dimension, ensuring the solver will work even if
missing values occur at 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*.
"""
# Define valid keyword arguments and their default values. This method
# is required since Python 2.7 cannot accept a variable argument list
# followed by a set of keyword arguments. For some reason both must be
# variable.
keywords = {"weights": None, "center": True, "ddof": 1}
for kwarg in kwargs.keys():
if kwarg not in keywords.keys():
raise EofError("invalid argument: %s" % kwarg)
weights = kwargs.get("weights", keywords["weights"])
center = kwargs.get("center", keywords["center"])
ddof = kwargs.get("ddof", keywords["ddof"])
# Record the number of datasets provided.
self._ndatasets = len(datasets)
# Initialise instance variables dealing with dataset shapes.
self._multirecords = list()
self._multishapes = list()
self._multislicers = list()
self._multichannels = list()
self._multidtypes = list()
slicebegin = 0
for dataset in datasets:
records = dataset.shape[0]
shape = dataset.shape[1:]
channels = np.product(shape)
slicer = slice(slicebegin, slicebegin + channels)
slicebegin += channels
self._multirecords.append(records)
self._multishapes.append(shape)
self._multislicers.append(slicer)
self._multichannels.append(channels)
self._multidtypes.append(dataset.dtype)
# Check that all fields have the same time dimension.
if not (np.array(self._multirecords) == self._multirecords[0]).all():
raise EofError("all datasets must have the same first dimension")
# Get the dtype that will be used for the data and weights. This will
# be the 'highest' dtype of those passed.
dtype = sorted(self._multidtypes, reverse=True)[0]
# Form a full array to pass to the EOF solver consisting of all the
# flat inputs.
nt = self._multirecords[0]
ns = self._multichannels.sum()
dataset = ma.empty([nt, ns], dtype=dtype)
for iset in xrange(self._ndatasets):
slicer = self._multislicers[iset]
channels = self._multichannels[iset]
dataset[:, slicer] = datasets[iset].reshape([nt, channels])
# Construct an array of weights the same shape as the data array.
if weights is not None:
if len(weights) != self._ndatasets:
raise EofError("number of weights and datasets differs")
if not filter(lambda i: False if i is None else True, weights):
# If every entry in the weights list is None then just pass
# None to the EofSolver __init__ method.
warr = None
else:
# Construct a spatial weights array.
warr = np.empty([1, ns], dtype=dtype)
for iset in xrange(self._ndatasets):
slicer = self._multislicers[iset]
if weights[iset] is None:
# If this dataset has no weights use 1 for the weight
# of all elements.
warr[:, slicer] = 1.
else:
# Otherwise use the weights. These need to be
# conformed to the correct dimensions.
channels = self._multichannels[iset]
try:
warr[:, slicer] = np.broadcast_arrays(
datasets[iset][0],
weights[iset])[1].reshape([channels])
except ValueError:
raise EofError("weights are invalid")
else:
# Just pass None if none of the input datasets have associated
# weights.
warr = None
# Create an EofSolver object to handle the computations.
self._solver = EofSolver(dataset, weights=warr, center=center, ddof=1)
class Eof(object):
"""EOF analysis (meta-data enabled :py:mod:`cdms2` interface)."""
def __init__(self, dataset, weights="none", center=True, ddof=1):
"""Create an Eof object.
**Argument:**
*dataset*
A :py:mod:`cdms2` variable containing the data to be
analyzed. Time must be the first dimension. Missing values
are allowed provided that they are constant with time (e.g.,
values of an oceanographic field over land).
**Optional arguments:**
*weights*
Sets the weighting method. The following values are
accepted:
* *"area"* : Square-root of grid cell area normalized by
total area. Requires a latitude-longitude grid to be
present in the input :py:mod:`cdms2` variable *dataset*.
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
(*"cos_lat"* is also accepted). Requires a latitude
dimension to be present in the input :py:mod:`cdms2`
variable *dataset*.
* *"none"* : Equal weights for all grid points (default).
* *None* : Same as *"none"*.
An array of weights may also be supplied instead of
specifying a weighting method.
*center*
If *True*, the mean along the first axis of the input data
set (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). Generally this option
should be set to *True* as the covariance interpretation
relies on input data being anomalies with a time-mean of 0.
A valid reson for turning this off would be if you have
already generated an anomaly data set. Setting to *True* has
the useful side-effect of propagating missing values along
the time-dimension, ensuring the solver will work even if
missing values occur at 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*.
**Examples:**
EOF analysis with area-weighting for the input field:
>>> from eof2 import Eof
>>> eofobj = Eof(field, weights="area")
"""
# Check that dataset is recognised by cdms2 as a variable.
if not cdms2.isVariable(dataset):
raise EofError("the input data must be a cdms2 variable")
# Store the time axis as an instance variable.
self._timeax = dataset.getTime()
# Verify that a time axis was found, getTime returns None when a
# time axis is not found.
if self._timeax is None:
raise EofError("time axis not found")
# Check the dimension order of the input, time must be the first
# dimension.
order = dataset.getOrder()
if order[0] != "t":
raise EofError("time must be the first dimension")
# Verify the presence of at least one spatial dimension. The
# instance variable channels will also be used as a partial axis
# list when constructing meta-data. It contains the spatial
# dimensions.
self._channels = dataset.getAxisList()
self._channels.remove(self._timeax)
if len(self._channels) < 1:
raise EofError("one or more spatial dimensions are required")
# Store the missing value attribute of the data set in an
# instance variable so that it is recoverable later.
self._missing_value = dataset.getMissing()
# Generate an appropriate set of weights for the input dataset. There
# are several weighting schemes. The "area" weighting scheme requires
# a latitude-longitude grid to be present, the "cos_lat" scheme only
# requires a latitude dimension.
if weights in ("none", None):
# No weights requested, set the weight array to None.
wtarray = None
else:
try:
# Generate a weights array of the appropriate kind, with a
# shape compatible with the data set.
scheme = weights.lower()
wtarray = weights_array(dataset, scheme=scheme)
except AttributeError:
# Weights is not a string, assume it is an array.
wtarray = weights
except EofToolError, err:
# Weights is not recognized, raise an error.
raise EofError(err)
# Cast the wtarray to the same type as the dataset. This prevents the
# promotion of 32-bit input to 64-bit on multiplication with the
# weight array when not required. This will fail with a AttributeError
# exception if the weights array is None, which it may be if no
# weighting was requested.
try:
wtarray = wtarray.astype(dataset.dtype)
except AttributeError:
pass
# Create an EofSolver object using appropriate arguments for this
# data set. The object will be used for the decomposition and
# for returning the results.
self._solver = EofSolver(dataset.asma(),
weights=wtarray,
center=center,
ddof=ddof)
self.neofs = self._solver.neofs