def build_from_data(self, X, f, df=None, avdim=None):
X, f, M, m = process_inputs_outputs(X, f)
self.X, self.f, self.m = X, f, m
# if gradients aren't available, estimate them from data
if df is None:
df = local_linear_gradients(X, f)
# compute the active subspace
ss = Subspaces()
ss.compute(df)
if avdim is not None:
ss.partition(avdim)
self.n = ss.W1.shape[1]
print 'Dimension of subspace is {:d}'.format(self.n)
# set up the active variable domain and map
if self.bndflag:
avdom = BoundedActiveVariableDomain(ss)
avmap = BoundedActiveVariableMap(avdom)
else:
avdom = UnboundedActiveVariableDomain(ss)
avmap = UnboundedActiveVariableMap(avdom)
# build the response surface
avrs = ActiveSubspaceResponseSurface(avmap)
avrs.train_with_data(X, f)
self.av_respsurf = avrs
def opg_subspace(X, f, weights):
"""Estimate active subspace with local linear models.
This approach is related to the sufficient dimension reduction method known
sometimes as the outer product of gradient method. See the 2001 paper
'Structure adaptive approach for dimension reduction' from Hristache, et al.
Parameters
----------
X : ndarray
M-by-m matrix of input samples, oriented as rows
f : ndarray
M-by-1 vector of output samples corresponding to the rows of `X`
weights : ndarray
M-by-1 weight vector, corresponds to numerical quadrature rule used to
estimate matrix whose eigenspaces define the active subspace
Returns
-------
e : ndarray
m-by-1 vector of eigenvalues
W : ndarray
m-by-m orthogonal matrix of eigenvectors
"""
X, f, M, m = process_inputs_outputs(X, f)
# Obtain gradient approximations using local linear regressions
df = local_linear_gradients(X, f, weights=weights)
# Use gradient approximations to compute active subspace
opg_weights = np.ones((df.shape[0], 1)) / df.shape[0]
e, W = active_subspace(df, opg_weights)
return e, W
def opg_subspace(X, f, weights):
"""Estimate active subspace with local linear models.
This approach is related to the sufficient dimension reduction method known
sometimes as the outer product of gradient method. See the 2001 paper
'Structure adaptive approach for dimension reduction' from Hristache, et al.
Parameters
----------
X : ndarray
M-by-m matrix of input samples, oriented as rows
f : ndarray
M-by-1 vector of output samples corresponding to the rows of `X`
weights : ndarray
M-by-1 weight vector, corresponds to numerical quadrature rule used to
estimate matrix whose eigenspaces define the active subspace
Returns
-------
e : ndarray
m-by-1 vector of eigenvalues
W : ndarray
m-by-m orthogonal matrix of eigenvectors
"""
X, f, M, m = process_inputs_outputs(X, f)
# Obtain gradient approximations using local linear regressions
df = local_linear_gradients(X, f, weights=weights)
# Use gradient approximations to compute active subspace
opg_weights = np.ones((df.shape[0], 1)) / df.shape[0]
e, W = active_subspace(df, opg_weights)
return e, W
def build_from_data(self, X, f, df=None):
X, M, m = process_inputs(X)
self.X, self.m, self.f = X, m, f
# if gradients aren't available, estimate them from data
if df is None:
df = local_linear_gradients(X, f)
self.df = df
# compute the active subspaces
self.subspaces = build_subspaces(df)
def opg_subspace(X, f, weights):
"""
TODO: docs
"""
X, f, M, m = process_inputs_outputs(X, f)
# Obtain gradient approximations using local linear regressions
df = local_linear_gradients(X, f, weights=weights)
# Use gradient approximations to compute active subspace
opg_weights = np.ones((df.shape[0], 1)) / df.shape[0]
e, W = active_subspace(df, opg_weights)
return e, W
def build_from_data(self, X, f, df=None, avdim=None):
"""
Build the active subspace-enabled model with input/output pairs.
:param ndarray X: M-by-m matrix with evaluations of the m-dimensional
simulation inputs.
:param ndarray f: M-by-1 matrix with corresponding simulation quantities
of interest.
:param ndarray df: M-by-m matrix that contains the gradients of the
simulation quantity of interest, oriented row-wise, that correspond
to the rows of `X`. If `df` is not present, then it is estimated
with crude local linear models using the pairs `X` and `f`.
:param int avdim: The dimension of the active subspace. If `avdim`
is not present, a crude heuristic is used to choose an active
subspace dimension based on the given data `X` and
`f`---and possible `df`.
**Notes**
This method follows these steps:
#. If `df` is None, estimate it with local linear models using the \
input/output pairs `X` and `f`.
#. Compute the active and inactive subspaces using `df`.
#. Train a response surface using `X` and `f` that exploits the active \
subspace.
"""
X, f, M, m = process_inputs_outputs(X, f)
# check if the given inputs satisfy the assumptions
if self.bounded_inputs:
if np.any(X) > 1.0 or np.any(X) < -1.0:
raise Exception('The supposedly bounded inputs exceed the \
bounds [-1,1].')
else:
if np.any(X) > 10.0 or np.any(X) < -10.0:
raise Exception('There is a very good chance that your \
unbounded inputs are not properly scaled.')
self.X, self.f, self.m = X, f, m
if df is not None:
df, M_df, m_df = process_inputs(df)
if m_df != m:
raise ValueError('The dimension of the gradients should be \
the same as the dimension of the inputs.')
else:
# if gradients aren't available, estimate them from data
df = local_linear_gradients(X, f)
# compute the active subspace
ss = Subspaces()
ss.compute(df)
if avdim is not None:
if not isinstance(avdim, int):
raise TypeError('avdim should be an integer.')
else:
ss.partition(avdim)
self.n = ss.W1.shape[1]
print 'The dimension of the active subspace is {:d}.'.format(self.n)
# set up the active variable domain and map
if self.bounded_inputs:
avdom = BoundedActiveVariableDomain(ss)
avmap = BoundedActiveVariableMap(avdom)
else:
avdom = UnboundedActiveVariableDomain(ss)
avmap = UnboundedActiveVariableMap(avdom)
# build the response surface
asrs = ActiveSubspaceResponseSurface(avmap)
asrs.train_with_data(X, f)
# set the R-squared coefficient
self.Rsqr = asrs.respsurf.Rsqr
self.as_respsurf = asrs