def chooseOptQoIs_verbose(grad_tensor,
qoiIndices=None,
num_qois_return=None,
num_optsets_return=None,
inner_prod_tol=1.0,
volume=False,
remove_zeros=True):
r"""
Given gradient vectors at some points (centers) in the parameter space, a
set of QoIs to choose from, and the number of desired QoIs to return, this
method returns the ``num_optsets_return`` best sets of QoIs with with
repsect to either the average condition number of the matrix formed by the
gradient vectors of each QoI map, or the average volume of the inverse
problem us this set of QoIs, computed as the product of the singular values
of the same matrix. This method is brute force, i.e., if the method is
given 10,000 QoIs and told to return the N best sets of 3, it will check all
10,000 choose 3 possible sets. See chooseOptQoIs_large for a less
computationally expensive approach.
:param grad_tensor: Gradient vectors at each point of interest in the
parameter space :math:`\Lambda` for each QoI map.
:type grad_tensor: :class:`np.ndarray` of shape (num_centers, num_qois,
Lambda_dim) where num_centers is the number of points in :math:`\Lambda`
we have approximated the gradient vectors and num_qois is the total
number of possible QoIs to choose from
:param qoiIndices: Set of QoIs to consider from grad_tensor. Default is
range(0, grad_tensor.shape[1])
:type qoiIndices: :class:`np.ndarray` of size (1, num QoIs to consider)
:param int num_qois_return: Number of desired QoIs to use in the
inverse problem. Default is Lambda_dim
:param int num_optsets_return: Number of best sets to return
Default is 10
:param boolean volume: If volume is True, use ``calculate_avg_volume``
to determine optimal QoIs
:param boolean remove_zeros: If True, ``find_unique_vecs`` will remove any
QoIs that have a zero gradient vector at atleast one point in
:math:`\Lambda`.
:rtype: tuple
:returns: (condnum_indices_mat, optsingvals) where condnum_indices_mat has
shape (num_optsets_return, num_qois_return+1) and optsingvals
has shape (num_centers, num_qois_return, num_optsets_return)
"""
num_centers = grad_tensor.shape[0]
Lambda_dim = grad_tensor.shape[2]
if qoiIndices is None:
qoiIndices = range(0, grad_tensor.shape[1])
if num_qois_return is None:
num_qois_return = Lambda_dim
if num_optsets_return is None:
num_optsets_return = 10
qoiIndices = find_unique_vecs(grad_tensor, inner_prod_tol, qoiIndices,
remove_zeros)
# Find all posible combinations of QoIs
if comm.rank == 0:
qoi_combs = np.array(
list(combinations(list(qoiIndices), num_qois_return)))
print 'Possible sets of QoIs : ', qoi_combs.shape[0]
qoi_combs = np.array_split(qoi_combs, comm.size)
else:
qoi_combs = None
# Scatter them throughout the processors
qoi_combs = comm.scatter(qoi_combs, root=0)
# For each combination, check the skewness and keep the sets
# that have the best skewness, i.e., smallest condition number
condnum_indices_mat = np.zeros([num_optsets_return, num_qois_return + 1])
condnum_indices_mat[:, 0] = np.inf
optsingvals_tensor = np.zeros(
[num_centers, num_qois_return, num_optsets_return])
for qoi_set in range(len(qoi_combs)):
if volume == False:
(current_condnum,
singvals) = calculate_avg_condnum(grad_tensor, qoi_combs[qoi_set])
else:
(current_condnum,
singvals) = calculate_avg_volume(grad_tensor, qoi_combs[qoi_set])
if current_condnum < condnum_indices_mat[-1, 0]:
condnum_indices_mat[-1, :] = np.append(np.array([current_condnum]),
qoi_combs[qoi_set])
order = condnum_indices_mat[:, 0].argsort()
condnum_indices_mat = condnum_indices_mat[order]
optsingvals_tensor[:, :, -1] = singvals
optsingvals_tensor = optsingvals_tensor[:, :, order]
# Wait for all processes to get to this point
comm.Barrier()
# Gather the best sets and condition numbers from each processor
condnum_indices_mat = np.array(comm.gather(condnum_indices_mat, root=0))
optsingvals_tensor = np.array(comm.gather(optsingvals_tensor, root=0))
# Find the num_optsets_return smallest condition numbers from all processors
if comm.rank == 0:
condnum_indices_mat = condnum_indices_mat.reshape(num_optsets_return * \
comm.size, num_qois_return + 1)
optsingvals_tensor = optsingvals_tensor.reshape(
num_centers, num_qois_return, num_optsets_return * comm.size)
order = condnum_indices_mat[:, 0].argsort()
condnum_indices_mat = condnum_indices_mat[order]
condnum_indices_mat = condnum_indices_mat[:num_optsets_return, :]
optsingvals_tensor = optsingvals_tensor[:, :, order]
optsingvals_tensor = optsingvals_tensor[:, :, :num_optsets_return]
condnum_indices_mat = comm.bcast(condnum_indices_mat, root=0)
optsingvals_tensor = comm.bcast(optsingvals_tensor, root=0)
return (condnum_indices_mat, optsingvals_tensor)
def find_good_sets(grad_tensor, good_sets_prev, unique_indices,
num_optsets_return, cond_tol, volume):
r"""
#TODO: Use the idea we only know vectors are with 10% accuracy to guide
inner_prod tol and condnum_tol.
Given gradient vectors at each center in the parameter space and given
good sets of size n - 1, return good sets of size n. That is, return
sets of size n that have average condition number less than some tolerance.
:param grad_tensor: Gradient vectors at each centers in the parameter
space :math:'\Lambda' for each QoI map.
:type grad_tensor: :class:`np.ndarray` of shape (num_centers,num_qois,Ldim)
where num_centers is the number of points in :math:'\Lambda' we have
approximated the gradient vectors, num_qois is the total number of
possible QoIs to choose from, Ldim is the dimension of :math:`\Lambda`.
:param good_sets_prev: Good sets of QoIs of size n - 1.
:type good_sets_prev: :class:`np.ndarray` of size (num_good_sets_prev, n - 1)
:param unique_indices: Unique QoIs to consider.
:type unique_indices: :class:'np.ndarray' of size (num_unique_qois, 1)
:param int num_optsets_return: Number of best sets to return
:param float cond_tol: Throw out all sets of QoIs with average condition
number greater than this.
:param boolean volume: If volume is True, use ``calculate_avg_volume``
to determine optimal QoIs
:rtype: tuple
:returns: (good_sets, best_sets, optsingvals_tensor) where good sets has
size (num_good_sets, n), best sets has size (num_optsets_return,
n + 1) and optsingvals_tensor has size (num_centers, n, Lambda_dim)
"""
num_centers = grad_tensor.shape[0]
Lambda_dim = grad_tensor.shape[2]
num_qois_return = good_sets_prev.shape[1] + 1
comm.Barrier()
# Initialize best sets and set all condition numbers large
best_sets = np.zeros([num_optsets_return, num_qois_return + 1])
best_sets[:, 0] = np.inf
good_sets = np.zeros([1, num_qois_return])
count_qois = 0
optsingvals_tensor = np.zeros(
[num_centers, num_qois_return, num_optsets_return])
# For each good set of size n - 1, find the possible sets of size n and
# compute the average condition number of each
count_qois = 0
for i in range(good_sets_prev.shape[0]):
min_ind = np.max(good_sets_prev[i, :])
# Find all possible combinations of QoIs that include this set of n - 1
if comm.rank == 0:
inds_notin_set = util.fix_dimensions_vector_2darray(list(set(\
unique_indices) - set(good_sets_prev[i, :])))
# Choose only the QoI indices > min_ind so we do not repeat sets
inds_notin_set = util.fix_dimensions_vector_2darray(inds_notin_set[\
inds_notin_set > min_ind])
qoi_combs = util.fix_dimensions_vector_2darray(np.append(np.tile(\
good_sets_prev[i, :], [inds_notin_set.shape[0], 1]),
inds_notin_set, axis=1))
qoi_combs = np.array_split(qoi_combs, comm.size)
else:
qoi_combs = None
# Scatter them throughout the processors
qoi_combs = comm.scatter(qoi_combs, root=0)
# For each combination, compute the average condition number and add the
# set to good_sets if it is less than cond_tol
for qoi_set in range(len(qoi_combs)):
count_qois += 1
curr_set = util.fix_dimensions_vector_2darray(qoi_combs[qoi_set])\
.transpose()
if volume == False:
(current_condnum,
singvals) = calculate_avg_condnum(grad_tensor,
qoi_combs[qoi_set])
else:
(current_condnum,
singvals) = calculate_avg_volume(grad_tensor,
qoi_combs[qoi_set])
# If its a good set, add it to good_sets
if current_condnum < cond_tol:
good_sets = np.append(good_sets, curr_set, axis=0)
# If the average condition number is less than the max condition
# number in our best_sets, add it to best_sets
if current_condnum < best_sets[-1, 0]:
best_sets[-1, :] = np.append(np.array([current_condnum]),
qoi_combs[qoi_set])
order = best_sets[:, 0].argsort()
best_sets = best_sets[order]
# Store the corresponding singular values
optsingvals_tensor[:, :, -1] = singvals
optsingvals_tensor = optsingvals_tensor[:, :, order]
# Wait for all processes to get to this point
comm.Barrier()
# Gather the best sets and condition numbers from each processor
good_sets = comm.gather(good_sets, root=0)
best_sets = np.array(comm.gather(best_sets, root=0))
count_qois = np.array(comm.gather(count_qois, root=0))
# Find the num_optsets_return smallest condition numbers from all processors
if comm.rank == 0:
# Organize the best sets
best_sets = best_sets.reshape(num_optsets_return * \
comm.size, num_qois_return + 1)
[temp, uniq_inds_best] = np.unique(best_sets[:, 0], return_index=True)
best_sets = best_sets[uniq_inds_best, :]
best_sets = best_sets[best_sets[:, 0].argsort()]
best_sets = best_sets[:num_optsets_return, :]
# Organize the good sets
good_sets_new = np.zeros([1, num_qois_return])
for each in good_sets:
good_sets_new = np.append(good_sets_new, each[1:], axis=0)
good_sets = good_sets_new
print 'Possible sets of QoIs of size %i : '%good_sets.shape[1],\
np.sum(count_qois)
print 'Good sets of QoIs of size %i : '%good_sets.shape[1],\
good_sets.shape[0] - 1
comm.Barrier()
best_sets = comm.bcast(best_sets, root=0)
good_sets = comm.bcast(good_sets, root=0)
return (good_sets[1:].astype(int), best_sets, optsingvals_tensor)
def find_good_sets(input_set, good_sets_prev, unique_indices,
num_optsets_return, measskew_tol, measure):
r"""
.. todo:: Use the idea we only know vectors are with 10% accuracy to guide
inner_prod tol and skewness_tol.
Given gradient vectors at each center in the parameter space and given
good sets of size (n - 1), return good sets of size n. That is, return
sets of size n that have average measure(skewness) less than some tolerance.
:param input_set: The input sample set. Make sure the attribute _jacobians
is not None.
:type input_set: :class:`~bet.sample.sample_set`
:param good_sets_prev: Good sets of QoIs of size n - 1.
:type good_sets_prev: :class:`np.ndarray` of size (num_good_sets_prev, n -
1)
:param unique_indices: Unique QoIs to consider.
:type unique_indices: :class:`np.ndarray` of size (num_unique_qois, 1)
:param int num_optsets_return: Number of best sets to return
:param float measskew_tol: Throw out all sets of QoIs with average
measure(skewness) number greater than this.
:param boolean measure: If measure is True, use ``calculate_avg_measure``
to determine optimal QoIs, else use ``calculate_avg_skewness``
:rtype: tuple
:returns: (good_sets, best_sets, optsingvals_tensor) where good sets has
size (num_good_sets, n), best sets has size (num_optsets_return,
n + 1) and optsingvals_tensor has size (num_centers, n, input_dim)
"""
if input_set._jacobians is None:
raise ValueError("You must have jacobians to use this method.")
num_centers = input_set._jacobians.shape[0]
num_qois_return = good_sets_prev.shape[1] + 1
comm.Barrier()
# Initialize best sets and set all skewness values large
best_sets = np.zeros([num_optsets_return, num_qois_return + 1])
best_sets[:, 0] = np.inf
good_sets = np.zeros([1, num_qois_return])
count_qois = 0
optsingvals_tensor = np.zeros(
[num_centers, num_qois_return, num_optsets_return])
# For each good set of size (n - 1), find the possible sets of size n and
# compute the average skewness of each
count_qois = 0
for i in xrange(good_sets_prev.shape[0]):
min_ind = np.max(good_sets_prev[i, :])
# Find all possible combinations of QoIs that include this set of
# (n - 1)
if comm.rank == 0:
inds_notin_set = util.fix_dimensions_vector_2darray(list(set(\
unique_indices) - set(good_sets_prev[i, :])))
# Choose only the QoI indices > min_ind so we do not repeat sets
inds_notin_set = util.fix_dimensions_vector_2darray(inds_notin_set[\
inds_notin_set > min_ind])
qoi_combs = util.fix_dimensions_vector_2darray(np.append(np.tile(\
good_sets_prev[i, :], [inds_notin_set.shape[0], 1]),
inds_notin_set, axis=1))
qoi_combs = np.array_split(qoi_combs, comm.size)
else:
qoi_combs = None
# Scatter them throughout the processors
qoi_combs = comm.scatter(qoi_combs, root=0)
# For each combination, compute the average measure(skewness) and add
# the set to good_sets if it is less than measskew_tol
for qoi_set in xrange(len(qoi_combs)):
count_qois += 1
curr_set = util.fix_dimensions_vector_2darray(qoi_combs[qoi_set])\
.transpose()
if measure is False:
(current_measskew,
singvals) = calculate_avg_skewness(input_set,
qoi_combs[qoi_set])
else:
(current_measskew,
singvals) = calculate_avg_measure(input_set,
qoi_combs[qoi_set])
# If its a good set, add it to good_sets
if current_measskew < measskew_tol:
good_sets = np.append(good_sets, curr_set, axis=0)
# If the average skewness is less than the maxskewness
# in our best_sets, add it to best_sets
if current_measskew < best_sets[-1, 0]:
best_sets[-1, :] = np.append(np.array([current_measskew]),
qoi_combs[qoi_set])
order = best_sets[:, 0].argsort()
best_sets = best_sets[order]
# Store the corresponding singular values
optsingvals_tensor[:, :, -1] = singvals
optsingvals_tensor = optsingvals_tensor[:, :, order]
# Wait for all processes to get to this point
comm.Barrier()
# Gather the best sets and skewness values from each processor
good_sets = comm.gather(good_sets, root=0)
best_sets = np.array(comm.gather(best_sets, root=0))
count_qois = np.array(comm.gather(count_qois, root=0))
# Find the num_optsets_return smallest skewness from all processors
if comm.rank == 0:
# Organize the best sets
best_sets = best_sets.reshape(num_optsets_return * \
comm.size, num_qois_return + 1)
[_, uniq_inds_best] = np.unique(best_sets[:, 0], return_index=True)
best_sets = best_sets[uniq_inds_best, :]
best_sets = best_sets[best_sets[:, 0].argsort()]
best_sets = best_sets[:num_optsets_return, :]
# Organize the good sets
good_sets_new = np.zeros([1, num_qois_return])
for each in good_sets:
good_sets_new = np.append(good_sets_new, each[1:], axis=0)
good_sets = good_sets_new
logging.info('Possible sets of QoIs of size {} : {}'.format(\
good_sets.shape[1], np.sum(count_qois)))
logging.info('Good sets of QoIs of size {} : {}'.format(\
good_sets.shape[1], good_sets.shape[0] - 1))
comm.Barrier()
best_sets = comm.bcast(best_sets, root=0)
good_sets = comm.bcast(good_sets, root=0)
return (good_sets[1:].astype(int), best_sets, optsingvals_tensor)
def chooseOptQoIs_verbose(grad_tensor, qoiIndices=None, num_qois_return=None, num_optsets_return=None):
r"""
Given gradient vectors at some points(centers) in the parameter space, a set
of QoIs to choose from, and the number of desired QoIs to return, this
method return the set of optimal QoIs to use in the inverse problem by
choosing the set with optimal skewness properties. Also a tensor that
represents the singualre values of the matrices formed by the gradient
vectors of the optimal QoIs at each center is returned.
:param grad_tensor: Gradient vectors at each point of interest in the
parameter space :math:`\Lambda` for each QoI map.
:type grad_tensor: :class:`np.ndarray` of shape (num_centers, num_qois,
Lambda_dim) where num_centers is the number of points in :math:`\Lambda`
we have approximated the gradient vectors and num_qois is the total
number of possible QoIs to choose from
:param qoiIndices: Set of QoIs to consider from grad_tensor. Default is
range(0, grad_tensor.shape[1])
:type qoiIndices: :class:`np.ndarray` of size (1, num QoIs to consider)
:param int num_qois_return: Number of desired QoIs to use in the
inverse problem. Default is Lambda_dim
:param int num_optsets_return: Number of best sets to return
Default is 10
:rtype: tuple
:returns: (condnum_indices_mat, optsingvals) where condnum_indices_mat has
shape (num_optsets_return, num_qois_return+1) and optsingvals
has shape (num_centers, num_qois_return, num_optsets_return)
"""
num_centers = grad_tensor.shape[0]
Lambda_dim = grad_tensor.shape[2]
if qoiIndices is None:
qoiIndices = range(0, grad_tensor.shape[1])
if num_qois_return is None:
num_qois_return = Lambda_dim
if num_optsets_return is None:
num_optsets_return = 10
# Find all posible combinations of QoIs
if comm.rank == 0:
qoi_combs = np.array(list(combinations(list(qoiIndices), num_qois_return)))
print "Possible sets of QoIs : ", qoi_combs.shape[0]
qoi_combs = np.array_split(qoi_combs, comm.size)
else:
qoi_combs = None
# Scatter them throughout the processors
qoi_combs = comm.scatter(qoi_combs, root=0)
# For each combination, check the skewness and keep the sets
# that have the best skewness, i.e., smallest condition number
condnum_indices_mat = np.zeros([num_optsets_return, num_qois_return + 1])
condnum_indices_mat[:, 0] = 1e11
optsingvals_tensor = np.zeros([num_centers, num_qois_return, num_optsets_return])
for qoi_set in range(len(qoi_combs)):
singvals = np.linalg.svd(grad_tensor[:, qoi_combs[qoi_set], :], compute_uv=False)
# Find the centers that have atleast one zero sinular value
indz = singvals[:, -1] == 0
indnz = singvals[:, -1] != 0
current_condnum = (
np.sum(singvals[indnz, 0] / singvals[indnz, -1], axis=0) + 1e9 * np.sum(indz)
) / singvals.shape[0]
if current_condnum < condnum_indices_mat[-1, 0]:
condnum_indices_mat[-1, :] = np.append(np.array([current_condnum]), qoi_combs[qoi_set])
order = condnum_indices_mat[:, 0].argsort()
condnum_indices_mat = condnum_indices_mat[order]
optsingvals_tensor[:, :, -1] = singvals
optsingvals_tensor = optsingvals_tensor[:, :, order]
# Wait for all processes to get to this point
comm.Barrier()
# Gather the best sets and condition numbers from each processor
condnum_indices_mat = np.array(comm.gather(condnum_indices_mat, root=0))
optsingvals_tensor = np.array(comm.gather(optsingvals_tensor, root=0))
# Find the num_optsets_return smallest condition numbers from all processors
if comm.rank == 0:
condnum_indices_mat = condnum_indices_mat.reshape(num_optsets_return * comm.size, num_qois_return + 1)
optsingvals_tensor = optsingvals_tensor.reshape(num_centers, num_qois_return, num_optsets_return * comm.size)
order = condnum_indices_mat[:, 0].argsort()
condnum_indices_mat = condnum_indices_mat[order]
condnum_indices_mat = condnum_indices_mat[:num_optsets_return, :]
optsingvals_tensor = optsingvals_tensor[:, :, order]
optsingvals_tensor = optsingvals_tensor[:, :, :num_optsets_return]
condnum_indices_mat = comm.bcast(condnum_indices_mat, root=0)
optsingvals_tensor = comm.bcast(optsingvals_tensor, root=0)
return (condnum_indices_mat, optsingvals_tensor)
def chooseOptQoIs_verbose(input_set,
qoiIndices=None,
num_qois_return=None,
num_optsets_return=None,
inner_prod_tol=1.0,
measure=False,
remove_zeros=True):
r"""
Given gradient vectors at some points (centers) in the parameter space, a
set of QoIs to choose from, and the number of desired QoIs to return, this
method returns the ``num_optsets_return`` best sets of QoIs with with
repsect to either the average measure of the matrix formed by the
gradient vectors of each QoI map, OR the average skewness of the inverse
image of this set of QoIs, computed as the product of the singular values
of the same matrix. This method is brute force, i.e., if the method is
given 10,000 QoIs and told to return the N best sets of 3, it will check all
10,000 choose 3 possible sets. See chooseOptQoIs_large for a less
computationally expensive approach.
:param input_set: The input sample set. Make sure the attribute _jacobians
is not None
:type input_set: :class:`~bet.sample.sample_set`
:param qoiIndices: Set of QoIs to consider. Default is
xrange(0, input_set._jacobians.shape[1])
:type qoiIndices: :class:`np.ndarray` of size (1, num QoIs to consider)
:param int num_qois_return: Number of desired QoIs to use in the
inverse problem. Default is input_dim
:param int num_optsets_return: Number of best sets to return
Default is 10
:param boolean measure: If measure is True, use ``calculate_avg_measure``
to determine optimal QoIs, else use ``calculate_avg_skewness``
:param boolean remove_zeros: If True, ``find_unique_vecs`` will remove any
QoIs that have a zero gradient
:rtype: `np.ndarray` of shape (num_optsets_returned, num_qois_returned + 1)
:returns: measure_skewness_indices_mat
"""
G = input_set._jacobians
if G is None:
raise ValueError("You must have jacobians to use this method.")
input_dim = input_set._dim
num_centers = G.shape[0]
if qoiIndices is None:
qoiIndices = xrange(0, G.shape[1])
if num_qois_return is None:
num_qois_return = input_dim
if num_optsets_return is None:
num_optsets_return = 10
# Remove QoIs that have zero gradients at any of the centers
qoiIndices = find_unique_vecs(input_set, inner_prod_tol, qoiIndices,
remove_zeros)
# Find all posible combinations of QoIs
if comm.rank == 0:
qoi_combs = np.array(
list(combinations(list(qoiIndices), num_qois_return)))
logging.info('Possible sets of QoIs : {}'.format(qoi_combs.shape[0]))
qoi_combs = np.array_split(qoi_combs, comm.size)
else:
qoi_combs = None
# Scatter them throughout the processors
qoi_combs = comm.scatter(qoi_combs, root=0)
# For each combination, check the skewness and keep the sets
# that have the smallest skewness
measure_skewness_indices_mat = np.zeros(
[num_optsets_return, num_qois_return + 1])
measure_skewness_indices_mat[:, 0] = np.inf
optsingvals_tensor = np.zeros(
[num_centers, num_qois_return, num_optsets_return])
for qoi_set in xrange(len(qoi_combs)):
if measure == False:
(current_measskew,
singvals) = calculate_avg_skewness(input_set, qoi_combs[qoi_set])
else:
(current_measskew,
singvals) = calculate_avg_measure(input_set, qoi_combs[qoi_set])
if current_measskew < measure_skewness_indices_mat[-1, 0]:
measure_skewness_indices_mat[-1, :] = np.append(np.array(\
[current_measskew]), qoi_combs[qoi_set])
order = measure_skewness_indices_mat[:, 0].argsort()
measure_skewness_indices_mat = measure_skewness_indices_mat[order]
optsingvals_tensor[:, :, -1] = singvals
optsingvals_tensor = optsingvals_tensor[:, :, order]
# Wait for all processes to get to this point
comm.Barrier()
# Gather the best sets and skewness values from each processor
measure_skewness_indices_mat = np.array(comm.gather(\
measure_skewness_indices_mat, root=0))
optsingvals_tensor = np.array(comm.gather(optsingvals_tensor, root=0))
# Find the num_optsets_return smallest skewness values from all processors
if comm.rank == 0:
measure_skewness_indices_mat = measure_skewness_indices_mat.reshape(\
num_optsets_return * comm.size, num_qois_return + 1)
optsingvals_tensor = optsingvals_tensor.reshape(
num_centers, num_qois_return, num_optsets_return * comm.size)
order = measure_skewness_indices_mat[:, 0].argsort()
measure_skewness_indices_mat = measure_skewness_indices_mat[order]
measure_skewness_indices_mat = measure_skewness_indices_mat[\
:num_optsets_return, :]
optsingvals_tensor = optsingvals_tensor[:, :, order]
optsingvals_tensor = optsingvals_tensor[:, :, :num_optsets_return]
measure_skewness_indices_mat = comm.bcast(measure_skewness_indices_mat,
root=0)
optsingvals_tensor = comm.bcast(optsingvals_tensor, root=0)
return (measure_skewness_indices_mat, optsingvals_tensor)
def find_good_sets(grad_tensor, good_sets_prev, unique_indices,
num_optsets_return, cond_tol, volume):
r"""
#TODO: Use the idea we only know vectors are with 10% accuracy to guide
inner_prod tol and condnum_tol.
Given gradient vectors at each center in the parameter space and given
good sets of size n - 1, return good sets of size n. That is, return
sets of size n that have average condition number less than some tolerance.
:param grad_tensor: Gradient vectors at each centers in the parameter
space :math:'\Lambda' for each QoI map.
:type grad_tensor: :class:`np.ndarray` of shape (num_centers,num_qois,Ldim)
where num_centers is the number of points in :math:'\Lambda' we have
approximated the gradient vectors, num_qois is the total number of
possible QoIs to choose from, Ldim is the dimension of :math:`\Lambda`.
:param good_sets_prev: Good sets of QoIs of size n - 1.
:type good_sets_prev: :class:`np.ndarray` of size (num_good_sets_prev, n - 1)
:param unique_indices: Unique QoIs to consider.
:type unique_indices: :class:'np.ndarray' of size (num_unique_qois, 1)
:param int num_optsets_return: Number of best sets to return
:param float cond_tol: Throw out all sets of QoIs with average condition
number greater than this.
:param boolean volume: If volume is True, use ``calculate_avg_volume``
to determine optimal QoIs
:rtype: tuple
:returns: (good_sets, best_sets, optsingvals_tensor) where good sets has
size (num_good_sets, n), best sets has size (num_optsets_return,
n + 1) and optsingvals_tensor has size (num_centers, n, Lambda_dim)
"""
num_centers = grad_tensor.shape[0]
Lambda_dim = grad_tensor.shape[2]
num_qois_return = good_sets_prev.shape[1] + 1
comm.Barrier()
# Initialize best sets and set all condition numbers large
best_sets = np.zeros([num_optsets_return, num_qois_return + 1])
best_sets[:, 0] = 1E99
good_sets = np.zeros([1, num_qois_return])
count_qois = 0
optsingvals_tensor = np.zeros([num_centers, num_qois_return,
num_optsets_return])
# For each good set of size n - 1, find the possible sets of size n and
# compute the average condition number of each
count_qois = 0
for i in range(good_sets_prev.shape[0]):
min_ind = np.max(good_sets_prev[i, :])
# Find all possible combinations of QoIs that include this set of n - 1
if comm.rank == 0:
inds_notin_set = util.fix_dimensions_vector_2darray(list(set(\
unique_indices) - set(good_sets_prev[i, :])))
# Choose only the QoI indices > min_ind so we do not repeat sets
inds_notin_set = util.fix_dimensions_vector_2darray(inds_notin_set[\
inds_notin_set > min_ind])
qoi_combs = util.fix_dimensions_vector_2darray(np.append(np.tile(\
good_sets_prev[i, :], [inds_notin_set.shape[0], 1]),
inds_notin_set, axis=1))
qoi_combs = np.array_split(qoi_combs, comm.size)
else:
qoi_combs = None
# Scatter them throughout the processors
qoi_combs = comm.scatter(qoi_combs, root=0)
# For each combination, compute the average condition number and add the
# set to good_sets if it is less than cond_tol
for qoi_set in range(len(qoi_combs)):
count_qois += 1
curr_set = util.fix_dimensions_vector_2darray(qoi_combs[qoi_set])\
.transpose()
if volume == False:
(current_condnum, singvals) = calculate_avg_condnum(grad_tensor,
qoi_combs[qoi_set])
else:
(current_condnum, singvals) = calculate_avg_volume(grad_tensor,
qoi_combs[qoi_set])
# If its a good set, add it to good_sets
if current_condnum < cond_tol:
good_sets = np.append(good_sets, curr_set, axis=0)
# If the average condition number is less than the max condition
# number in our best_sets, add it to best_sets
if current_condnum < best_sets[-1, 0]:
best_sets[-1, :] = np.append(np.array([current_condnum]),
qoi_combs[qoi_set])
order = best_sets[:, 0].argsort()
best_sets = best_sets[order]
# Store the corresponding singular values
optsingvals_tensor[:, :, -1] = singvals
optsingvals_tensor = optsingvals_tensor[:, :, order]
# Wait for all processes to get to this point
comm.Barrier()
# Gather the best sets and condition numbers from each processor
good_sets = comm.gather(good_sets, root=0)
best_sets = np.array(comm.gather(best_sets, root=0))
count_qois = np.array(comm.gather(count_qois, root=0))
# Find the num_optsets_return smallest condition numbers from all processors
if comm.rank == 0:
# Organize the best sets
best_sets = best_sets.reshape(num_optsets_return * \
comm.size, num_qois_return + 1)
[temp, uniq_inds_best] = np.unique(best_sets[:, 0], return_index=True)
best_sets = best_sets[uniq_inds_best, :]
best_sets = best_sets[best_sets[:, 0].argsort()]
best_sets = best_sets[:num_optsets_return, :]
# Organize the good sets
good_sets_new = np.zeros([1, num_qois_return])
for each in good_sets:
good_sets_new = np.append(good_sets_new, each[1:], axis=0)
good_sets = good_sets_new
print 'Possible sets of QoIs of size %i : '%good_sets.shape[1],\
np.sum(count_qois)
print 'Good sets of QoIs of size %i : '%good_sets.shape[1],\
good_sets.shape[0] - 1
comm.Barrier()
best_sets = comm.bcast(best_sets, root=0)
good_sets = comm.bcast(good_sets, root=0)
return (good_sets[1:].astype(int), best_sets, optsingvals_tensor)
def chooseOptQoIs_verbose(grad_tensor, qoiIndices=None, num_qois_return=None,
num_optsets_return=None, inner_prod_tol=1.0, volume=False,
remove_zeros=True):
r"""
Given gradient vectors at some points (centers) in the parameter space, a
set of QoIs to choose from, and the number of desired QoIs to return, this
method returns the ``num_optsets_return`` best sets of QoIs with with
repsect to either the average condition number of the matrix formed by the
gradient vectors of each QoI map, or the average volume of the inverse
problem us this set of QoIs, computed as the product of the singular values
of the same matrix. This method is brute force, i.e., if the method is
given 10,000 QoIs and told to return the N best sets of 3, it will check all
10,000 choose 3 possible sets. See chooseOptQoIs_large for a less
computationally expensive approach.
:param grad_tensor: Gradient vectors at each point of interest in the
parameter space :math:`\Lambda` for each QoI map.
:type grad_tensor: :class:`np.ndarray` of shape (num_centers, num_qois,
Lambda_dim) where num_centers is the number of points in :math:`\Lambda`
we have approximated the gradient vectors and num_qois is the total
number of possible QoIs to choose from
:param qoiIndices: Set of QoIs to consider from grad_tensor. Default is
range(0, grad_tensor.shape[1])
:type qoiIndices: :class:`np.ndarray` of size (1, num QoIs to consider)
:param int num_qois_return: Number of desired QoIs to use in the
inverse problem. Default is Lambda_dim
:param int num_optsets_return: Number of best sets to return
Default is 10
:param boolean volume: If volume is True, use ``calculate_avg_volume``
to determine optimal QoIs
:param boolean remove_zeros: If True, ``find_unique_vecs`` will remove any
QoIs that have a zero gradient vector at atleast one point in
:math:`\Lambda`.
:rtype: tuple
:returns: (condnum_indices_mat, optsingvals) where condnum_indices_mat has
shape (num_optsets_return, num_qois_return+1) and optsingvals
has shape (num_centers, num_qois_return, num_optsets_return)
"""
num_centers = grad_tensor.shape[0]
Lambda_dim = grad_tensor.shape[2]
if qoiIndices is None:
qoiIndices = range(0, grad_tensor.shape[1])
if num_qois_return is None:
num_qois_return = Lambda_dim
if num_optsets_return is None:
num_optsets_return = 10
qoiIndices = find_unique_vecs(grad_tensor, inner_prod_tol, qoiIndices,
remove_zeros)
# Find all posible combinations of QoIs
if comm.rank == 0:
qoi_combs = np.array(list(combinations(list(qoiIndices),
num_qois_return)))
print 'Possible sets of QoIs : ', qoi_combs.shape[0]
qoi_combs = np.array_split(qoi_combs, comm.size)
else:
qoi_combs = None
# Scatter them throughout the processors
qoi_combs = comm.scatter(qoi_combs, root=0)
# For each combination, check the skewness and keep the sets
# that have the best skewness, i.e., smallest condition number
condnum_indices_mat = np.zeros([num_optsets_return, num_qois_return + 1])
condnum_indices_mat[:, 0] = 1E99
optsingvals_tensor = np.zeros([num_centers, num_qois_return,
num_optsets_return])
for qoi_set in range(len(qoi_combs)):
if volume == False:
(current_condnum, singvals) = calculate_avg_condnum(grad_tensor,
qoi_combs[qoi_set])
else:
(current_condnum, singvals) = calculate_avg_volume(grad_tensor,
qoi_combs[qoi_set])
if current_condnum < condnum_indices_mat[-1, 0]:
condnum_indices_mat[-1, :] = np.append(np.array([current_condnum]),
qoi_combs[qoi_set])
order = condnum_indices_mat[:, 0].argsort()
condnum_indices_mat = condnum_indices_mat[order]
optsingvals_tensor[:, :, -1] = singvals
optsingvals_tensor = optsingvals_tensor[:, :, order]
# Wait for all processes to get to this point
comm.Barrier()
# Gather the best sets and condition numbers from each processor
condnum_indices_mat = np.array(comm.gather(condnum_indices_mat, root=0))
optsingvals_tensor = np.array(comm.gather(optsingvals_tensor, root=0))
# Find the num_optsets_return smallest condition numbers from all processors
if comm.rank == 0:
condnum_indices_mat = condnum_indices_mat.reshape(num_optsets_return * \
comm.size, num_qois_return + 1)
optsingvals_tensor = optsingvals_tensor.reshape(num_centers,
num_qois_return, num_optsets_return * comm.size)
order = condnum_indices_mat[:, 0].argsort()
condnum_indices_mat = condnum_indices_mat[order]
condnum_indices_mat = condnum_indices_mat[:num_optsets_return, :]
optsingvals_tensor = optsingvals_tensor[:, :, order]
optsingvals_tensor = optsingvals_tensor[:, :, :num_optsets_return]
condnum_indices_mat = comm.bcast(condnum_indices_mat, root=0)
optsingvals_tensor = comm.bcast(optsingvals_tensor, root=0)
return (condnum_indices_mat, optsingvals_tensor)
def find_good_sets(input_set, good_sets_prev, unique_indices,
num_optsets_return, measskew_tol, measure):
r"""
.. todo:: Use the idea we only know vectors are with 10% accuracy to guide
inner_prod tol and skewness_tol.
Given gradient vectors at each center in the parameter space and given
good sets of size (n - 1), return good sets of size n. That is, return
sets of size n that have average measure(skewness) less than some tolerance.
:param input_set: The input sample set. Make sure the attribute _jacobians
is not None.
:type input_set: :class:`~bet.sample.sample_set`
:param good_sets_prev: Good sets of QoIs of size n - 1.
:type good_sets_prev: :class:`np.ndarray` of size (num_good_sets_prev, n -
1)
:param unique_indices: Unique QoIs to consider.
:type unique_indices: :class:`np.ndarray` of size (num_unique_qois, 1)
:param int num_optsets_return: Number of best sets to return
:param float measskew_tol: Throw out all sets of QoIs with average
measure(skewness) number greater than this.
:param boolean measure: If measure is True, use ``calculate_avg_measure``
to determine optimal QoIs, else use ``calculate_avg_skewness``
:rtype: tuple
:returns: (good_sets, best_sets, optsingvals_tensor) where good sets has
size (num_good_sets, n), best sets has size (num_optsets_return,
n + 1) and optsingvals_tensor has size (num_centers, n, input_dim)
"""
if input_set._jacobians is None:
raise ValueError("You must have jacobians to use this method.")
num_centers = input_set._jacobians.shape[0]
num_qois_return = good_sets_prev.shape[1] + 1
comm.Barrier()
# Initialize best sets and set all skewness values large
best_sets = np.zeros([num_optsets_return, num_qois_return + 1])
best_sets[:, 0] = np.inf
good_sets = np.zeros([1, num_qois_return])
count_qois = 0
optsingvals_tensor = np.zeros([num_centers, num_qois_return,
num_optsets_return])
# For each good set of size (n - 1), find the possible sets of size n and
# compute the average skewness of each
count_qois = 0
for i in range(good_sets_prev.shape[0]):
min_ind = np.max(good_sets_prev[i, :])
# Find all possible combinations of QoIs that include this set of
# (n - 1)
if comm.rank == 0:
inds_notin_set = util.fix_dimensions_vector_2darray(list(set(
unique_indices) - set(good_sets_prev[i, :])))
# Choose only the QoI indices > min_ind so we do not repeat sets
inds_notin_set = util.fix_dimensions_vector_2darray(inds_notin_set[
inds_notin_set > min_ind])
qoi_combs = util.fix_dimensions_vector_2darray(np.append(np.tile(
good_sets_prev[i, :], [inds_notin_set.shape[0], 1]),
inds_notin_set, axis=1))
qoi_combs = np.array_split(qoi_combs, comm.size)
else:
qoi_combs = None
# Scatter them throughout the processors
qoi_combs = comm.scatter(qoi_combs, root=0)
# For each combination, compute the average measure(skewness) and add
# the set to good_sets if it is less than measskew_tol
for qoi_set in range(len(qoi_combs)):
count_qois += 1
curr_set = util.fix_dimensions_vector_2darray(qoi_combs[qoi_set])\
.transpose()
if measure is False:
(current_measskew, singvals) = calculate_avg_skewness(input_set,
qoi_combs[qoi_set])
else:
(current_measskew, singvals) = calculate_avg_measure(input_set,
qoi_combs[qoi_set])
# If its a good set, add it to good_sets
if current_measskew < measskew_tol:
good_sets = np.append(good_sets, curr_set, axis=0)
# If the average skewness is less than the maxskewness
# in our best_sets, add it to best_sets
if current_measskew < best_sets[-1, 0]:
best_sets[-1, :] = np.append(np.array([current_measskew]),
qoi_combs[qoi_set])
order = best_sets[:, 0].argsort()
best_sets = best_sets[order]
# Store the corresponding singular values
optsingvals_tensor[:, :, -1] = singvals
optsingvals_tensor = optsingvals_tensor[:, :, order]
# Wait for all processes to get to this point
comm.Barrier()
# Gather the best sets and skewness values from each processor
good_sets = comm.gather(good_sets, root=0)
best_sets = np.array(comm.gather(best_sets, root=0))
count_qois = np.array(comm.gather(count_qois, root=0))
# Find the num_optsets_return smallest skewness from all processors
if comm.rank == 0:
# Organize the best sets
best_sets = best_sets.reshape(num_optsets_return *
comm.size, num_qois_return + 1)
[_, uniq_inds_best] = np.unique(best_sets[:, 0], return_index=True)
best_sets = best_sets[uniq_inds_best, :]
best_sets = best_sets[best_sets[:, 0].argsort()]
best_sets = best_sets[:num_optsets_return, :]
# Organize the good sets
good_sets_new = np.zeros([1, num_qois_return])
for each in good_sets:
good_sets_new = np.append(good_sets_new, each[1:], axis=0)
good_sets = good_sets_new
logging.info('Possible sets of QoIs of size {} : {}'.format(
good_sets.shape[1], np.sum(count_qois)))
logging.info('Good sets of QoIs of size {} : {}'.format(
good_sets.shape[1], good_sets.shape[0] - 1))
comm.Barrier()
best_sets = comm.bcast(best_sets, root=0)
good_sets = comm.bcast(good_sets, root=0)
return (good_sets[1:].astype(int), best_sets, optsingvals_tensor)
def chooseOptQoIs_verbose(input_set, qoiIndices=None, num_qois_return=None,
num_optsets_return=None, inner_prod_tol=1.0, measure=False,
remove_zeros=True):
r"""
Given gradient vectors at some points (centers) in the parameter space, a
set of QoIs to choose from, and the number of desired QoIs to return, this
method returns the ``num_optsets_return`` best sets of QoIs with with
repsect to either the average measure of the matrix formed by the
gradient vectors of each QoI map, OR the average skewness of the inverse
image of this set of QoIs, computed as the product of the singular values
of the same matrix. This method is brute force, i.e., if the method is
given 10,000 QoIs and told to return the N best sets of 3, it will check all
10,000 choose 3 possible sets. See chooseOptQoIs_large for a less
computationally expensive approach.
:param input_set: The input sample set. Make sure the attribute _jacobians
is not None
:type input_set: :class:`~bet.sample.sample_set`
:param qoiIndices: Set of QoIs to consider. Default is
xrange(0, input_set._jacobians.shape[1])
:type qoiIndices: :class:`np.ndarray` of size (1, num QoIs to consider)
:param int num_qois_return: Number of desired QoIs to use in the
inverse problem. Default is input_dim
:param int num_optsets_return: Number of best sets to return
Default is 10
:param boolean measure: If measure is True, use ``calculate_avg_measure``
to determine optimal QoIs, else use ``calculate_avg_skewness``
:param boolean remove_zeros: If True, ``find_unique_vecs`` will remove any
QoIs that have a zero gradient
:rtype: `np.ndarray` of shape (num_optsets_returned, num_qois_returned + 1)
:returns: measure_skewness_indices_mat
"""
G = input_set._jacobians
if G is None:
raise ValueError("You must have jacobians to use this method.")
input_dim = input_set._dim
num_centers = G.shape[0]
if qoiIndices is None:
qoiIndices = range(0, G.shape[1])
if num_qois_return is None:
num_qois_return = input_dim
if num_optsets_return is None:
num_optsets_return = 10
# Remove QoIs that have zero gradients at any of the centers
qoiIndices = find_unique_vecs(input_set, inner_prod_tol, qoiIndices,
remove_zeros)
# Find all posible combinations of QoIs
if comm.rank == 0:
qoi_combs = np.array(list(combinations(list(qoiIndices),
num_qois_return)))
logging.info('Possible sets of QoIs : {}'.format(qoi_combs.shape[0]))
qoi_combs = np.array_split(qoi_combs, comm.size)
else:
qoi_combs = None
# Scatter them throughout the processors
qoi_combs = comm.scatter(qoi_combs, root=0)
# For each combination, check the skewness and keep the sets
# that have the smallest skewness
measure_skewness_indices_mat = np.zeros([num_optsets_return,
num_qois_return + 1])
measure_skewness_indices_mat[:, 0] = np.inf
optsingvals_tensor = np.zeros([num_centers, num_qois_return,
num_optsets_return])
for qoi_set in range(len(qoi_combs)):
if measure == False:
(current_measskew, singvals) = calculate_avg_skewness(input_set,
qoi_combs[qoi_set])
else:
(current_measskew, singvals) = calculate_avg_measure(input_set,
qoi_combs[qoi_set])
if current_measskew < measure_skewness_indices_mat[-1, 0]:
measure_skewness_indices_mat[-1, :] = np.append(np.array(
[current_measskew]), qoi_combs[qoi_set])
order = measure_skewness_indices_mat[:, 0].argsort()
measure_skewness_indices_mat = measure_skewness_indices_mat[order]
optsingvals_tensor[:, :, -1] = singvals
optsingvals_tensor = optsingvals_tensor[:, :, order]
# Wait for all processes to get to this point
comm.Barrier()
# Gather the best sets and skewness values from each processor
measure_skewness_indices_mat = np.array(comm.gather(
measure_skewness_indices_mat, root=0))
optsingvals_tensor = np.array(comm.gather(optsingvals_tensor, root=0))
# Find the num_optsets_return smallest skewness values from all processors
if comm.rank == 0:
measure_skewness_indices_mat = measure_skewness_indices_mat.reshape(
num_optsets_return * comm.size, num_qois_return + 1)
optsingvals_tensor = optsingvals_tensor.reshape(num_centers,
num_qois_return, num_optsets_return * comm.size)
order = measure_skewness_indices_mat[:, 0].argsort()
measure_skewness_indices_mat = measure_skewness_indices_mat[order]
measure_skewness_indices_mat = measure_skewness_indices_mat[
:num_optsets_return, :]
optsingvals_tensor = optsingvals_tensor[:, :, order]
optsingvals_tensor = optsingvals_tensor[:, :, :num_optsets_return]
measure_skewness_indices_mat = comm.bcast(measure_skewness_indices_mat,
root=0)
optsingvals_tensor = comm.bcast(optsingvals_tensor, root=0)
return (measure_skewness_indices_mat, optsingvals_tensor)
