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 loadmat(save_file, lb_model=None, hot_start=None, num_chains=None):
"""
Loads data from ``save_file`` into a
:class:`~bet.sampling.adaptiveSampling.sampler` object.
:param string save_file: file name
:param lb_model: runs the model at a given set of parameter samples, (N,
ndim), and returns data (N, mdim)
:param int hot_start: Flag whether or not hot start the sampling
chains from a previous set of chains. Note that ``num_chains`` must
be the same, but ``num_chains_pproc`` need not be the same. 0 -
cold start, 1 - hot start from uncompleted run, 2 - hot
start from finished run
:param int num_chains: total number of chains of samples
:param callable lb_model: runs the model at a given set of parameter
samples, (N, ndim), and returns data (N, mdim)
:rtype: tuple of (:class:`bet.sampling.adaptiveSampling.sampler`,
:class:`bet.sample.discretization`, :class:`numpy.ndarray`,
:class:`numpy.ndarray`)
:returns: (``sampler``, ``discretization``, ``all_step_ratios``,
``kern_old``)
"""
print hot_start
if hot_start is None:
hot_start = 1
# LOAD FILES
if hot_start == 1: # HOT START FROM PARTIAL RUN
if comm.rank == 0:
logging.info("HOT START from partial run")
# Find and open save files
save_dir = os.path.dirname(save_file)
base_name = os.path.basename(save_file)
mdat_files = glob.glob(os.path.join(save_dir,
"proc*_{}".format(base_name)))
if len(mdat_files) > 0:
tmp_mdat = sio.loadmat(mdat_files[0])
else:
tmp_mdat = sio.loadmat(save_file)
if num_chains is None:
num_chains = np.squeeze(tmp_mdat['num_chains'])
num_chains_pproc = num_chains / comm.size
if len(mdat_files) == 0:
logging.info("HOT START using serial file")
mdat = sio.loadmat(save_file)
if num_chains is None:
num_chains = np.squeeze(mdat['num_chains'])
num_chains_pproc = num_chains / comm.size
disc = sample.load_discretization(save_file)
kern_old = np.squeeze(mdat['kern_old'])
all_step_ratios = np.squeeze(mdat['step_ratios'])
chain_length = disc.check_nums()/num_chains
if all_step_ratios.shape == (num_chains,
chain_length):
msg = "Serial file, from completed"
msg += " run updating hot_start"
hot_start = 2
# reshape if parallel
if comm.size > 1:
temp_input = np.reshape(disc._input_sample_set.\
get_values(), (num_chains,
chain_length, -1), 'F')
temp_output = np.reshape(disc._output_sample_set.\
get_values(), (num_chains,
chain_length, -1), 'F')
all_step_ratios = np.reshape(all_step_ratios,
(num_chains, -1), 'F')
elif hot_start == 1 and len(mdat_files) == comm.size:
logging.info("HOT START using parallel files (same nproc)")
# if the number of processors is the same then set mdat to
# be the one with the matching processor number (doesn't
# really matter)
disc = sample.load_discretization(mdat_files[comm.rank])
kern_old = np.squeeze(tmp_mdat['kern_old'])
all_step_ratios = np.squeeze(tmp_mdat['step_ratios'])
elif hot_start == 1 and len(mdat_files) != comm.size:
logging.info("HOT START using parallel files (diff nproc)")
# Determine how many processors the previous data used
# otherwise gather the data from mdat and then scatter
# among the processors and update mdat
mdat_files_local = comm.scatter(mdat_files)
mdat_local = [sio.loadmat(m) for m in mdat_files_local]
disc_local = [sample.load_discretization(m) for m in\
mdat_files_local]
mdat_list = comm.allgather(mdat_local)
disc_list = comm.allgather(disc_local)
mdat_global = []
disc_global = []
# instead of a list of lists, create a list of mdat
for mlist, dlist in zip(mdat_list, disc_list):
mdat_global.extend(mlist)
disc_global.extend(dlist)
# get num_proc and num_chains_pproc for previous run
old_num_proc = max((len(mdat_list), 1))
old_num_chains_pproc = num_chains/old_num_proc
# get batch size and/or number of dimensions
chain_length = disc_global[0].check_nums()/\
old_num_chains_pproc
disc = disc_global[0].copy()
# create lists of local data
temp_input = []
temp_output = []
all_step_ratios = []
kern_old = []
# RESHAPE old_num_chains_pproc, chain_length(or batch), dim
for mdat, disc_local in zip(mdat_global, disc_local):
temp_input.append(np.reshape(disc_local.\
_input_sample_set.get_values_local(),
(old_num_chains_pproc, chain_length, -1), 'F'))
temp_output.append(np.reshape(disc_local.\
_output_sample_set.get_values_local(),
(old_num_chains_pproc, chain_length, -1), 'F'))
all_step_ratios.append(np.reshape(mdat['step_ratios'],
(old_num_chains_pproc, chain_length, -1), 'F'))
kern_old.append(np.reshape(mdat['kern_old'],
(old_num_chains_pproc,), 'F'))
# turn into arrays
temp_input = np.concatenate(temp_input)
temp_output = np.concatenate(temp_output)
all_step_ratios = np.concatenate(all_step_ratios)
kern_old = np.concatenate(kern_old)
if hot_start == 2: # HOT START FROM COMPLETED RUN:
if comm.rank == 0:
logging.info("HOT START from completed run")
mdat = sio.loadmat(save_file)
if num_chains is None:
num_chains = np.squeeze(mdat['num_chains'])
num_chains_pproc = num_chains / comm.size
disc = sample.load_discretization(save_file)
kern_old = np.squeeze(mdat['kern_old'])
all_step_ratios = np.squeeze(mdat['step_ratios'])
chain_length = disc.check_nums()/num_chains
# reshape if parallel
if comm.size > 1:
temp_input = np.reshape(disc._input_sample_set.\
get_values(), (num_chains, chain_length,
-1), 'F')
temp_output = np.reshape(disc._output_sample_set.\
get_values(), (num_chains, chain_length,
-1), 'F')
all_step_ratios = np.reshape(all_step_ratios,
(num_chains, chain_length), 'F')
# SPLIT DATA IF NECESSARY
if comm.size > 1 and (hot_start == 2 or (hot_start == 1 and \
len(mdat_files) != comm.size)):
# Use split to split along num_chains and set *._values_local
disc._input_sample_set.set_values_local(np.reshape(np.split(\
temp_input, comm.size, 0)[comm.rank],
(num_chains_pproc*chain_length, -1), 'F'))
disc._output_sample_set.set_values_local(np.reshape(np.split(\
temp_output, comm.size, 0)[comm.rank],
(num_chains_pproc*chain_length, -1), 'F'))
all_step_ratios = np.reshape(np.split(all_step_ratios,
comm.size, 0)[comm.rank],
(num_chains_pproc*chain_length,), 'F')
kern_old = np.reshape(np.split(kern_old, comm.size,
0)[comm.rank], (num_chains_pproc,), 'F')
else:
all_step_ratios = np.reshape(all_step_ratios, (-1,), 'F')
print chain_length*num_chains, chain_length, lb_model
new_sampler = sampler(chain_length*num_chains, chain_length, lb_model)
return (new_sampler, disc, all_step_ratios, kern_old)
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(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 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(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 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 loadmat(save_file, lb_model=None, hot_start=None, num_chains=None):
"""
Loads data from ``save_file`` into a
:class:`~bet.sampling.adaptiveSampling.sampler` object.
:param string save_file: file name
:param lb_model: runs the model at a given set of parameter samples, (N,
ndim), and returns data (N, mdim)
:param int hot_start: Flag whether or not hot start the sampling
chains from a previous set of chains. Note that ``num_chains`` must
be the same, but ``num_chains_pproc`` need not be the same. 0 -
cold start, 1 - hot start from uncompleted run, 2 - hot
start from finished run
:param int num_chains: total number of chains of samples
:param callable lb_model: runs the model at a given set of parameter
samples, (N, ndim), and returns data (N, mdim)
:rtype: tuple of (:class:`bet.sampling.adaptiveSampling.sampler`,
:class:`bet.sample.discretization`, :class:`numpy.ndarray`,
:class:`numpy.ndarray`)
:returns: (``sampler``, ``discretization``, ``all_step_ratios``,
``kern_old``)
"""
print hot_start
if hot_start is None:
hot_start = 1
# LOAD FILES
if hot_start == 1: # HOT START FROM PARTIAL RUN
if comm.rank == 0:
logging.info("HOT START from partial run")
# Find and open save files
save_dir = os.path.dirname(save_file)
base_name = os.path.basename(save_file)
mdat_files = glob.glob(
os.path.join(save_dir, "proc*_{}".format(base_name)))
if len(mdat_files) > 0:
tmp_mdat = sio.loadmat(mdat_files[0])
else:
tmp_mdat = sio.loadmat(save_file)
if num_chains is None:
num_chains = np.squeeze(tmp_mdat['num_chains'])
num_chains_pproc = num_chains / comm.size
if len(mdat_files) == 0:
logging.info("HOT START using serial file")
mdat = sio.loadmat(save_file)
if num_chains is None:
num_chains = np.squeeze(mdat['num_chains'])
num_chains_pproc = num_chains / comm.size
disc = sample.load_discretization(save_file)
kern_old = np.squeeze(mdat['kern_old'])
all_step_ratios = np.squeeze(mdat['step_ratios'])
chain_length = disc.check_nums() / num_chains
if all_step_ratios.shape == (num_chains, chain_length):
msg = "Serial file, from completed"
msg += " run updating hot_start"
hot_start = 2
# reshape if parallel
if comm.size > 1:
temp_input = np.reshape(disc._input_sample_set.\
get_values(), (num_chains,
chain_length, -1), 'F')
temp_output = np.reshape(disc._output_sample_set.\
get_values(), (num_chains,
chain_length, -1), 'F')
all_step_ratios = np.reshape(all_step_ratios, (num_chains, -1),
'F')
elif hot_start == 1 and len(mdat_files) == comm.size:
logging.info("HOT START using parallel files (same nproc)")
# if the number of processors is the same then set mdat to
# be the one with the matching processor number (doesn't
# really matter)
disc = sample.load_discretization(mdat_files[comm.rank])
kern_old = np.squeeze(tmp_mdat['kern_old'])
all_step_ratios = np.squeeze(tmp_mdat['step_ratios'])
elif hot_start == 1 and len(mdat_files) != comm.size:
logging.info("HOT START using parallel files (diff nproc)")
# Determine how many processors the previous data used
# otherwise gather the data from mdat and then scatter
# among the processors and update mdat
mdat_files_local = comm.scatter(mdat_files)
mdat_local = [sio.loadmat(m) for m in mdat_files_local]
disc_local = [sample.load_discretization(m) for m in\
mdat_files_local]
mdat_list = comm.allgather(mdat_local)
disc_list = comm.allgather(disc_local)
mdat_global = []
disc_global = []
# instead of a list of lists, create a list of mdat
for mlist, dlist in zip(mdat_list, disc_list):
mdat_global.extend(mlist)
disc_global.extend(dlist)
# get num_proc and num_chains_pproc for previous run
old_num_proc = max((len(mdat_list), 1))
old_num_chains_pproc = num_chains / old_num_proc
# get batch size and/or number of dimensions
chain_length = disc_global[0].check_nums()/\
old_num_chains_pproc
disc = disc_global[0].copy()
# create lists of local data
temp_input = []
temp_output = []
all_step_ratios = []
kern_old = []
# RESHAPE old_num_chains_pproc, chain_length(or batch), dim
for mdat, disc_local in zip(mdat_global, disc_local):
temp_input.append(np.reshape(disc_local.\
_input_sample_set.get_values_local(),
(old_num_chains_pproc, chain_length, -1), 'F'))
temp_output.append(np.reshape(disc_local.\
_output_sample_set.get_values_local(),
(old_num_chains_pproc, chain_length, -1), 'F'))
all_step_ratios.append(
np.reshape(mdat['step_ratios'],
(old_num_chains_pproc, chain_length, -1), 'F'))
kern_old.append(
np.reshape(mdat['kern_old'], (old_num_chains_pproc, ),
'F'))
# turn into arrays
temp_input = np.concatenate(temp_input)
temp_output = np.concatenate(temp_output)
all_step_ratios = np.concatenate(all_step_ratios)
kern_old = np.concatenate(kern_old)
if hot_start == 2: # HOT START FROM COMPLETED RUN:
if comm.rank == 0:
logging.info("HOT START from completed run")
mdat = sio.loadmat(save_file)
if num_chains is None:
num_chains = np.squeeze(mdat['num_chains'])
num_chains_pproc = num_chains / comm.size
disc = sample.load_discretization(save_file)
kern_old = np.squeeze(mdat['kern_old'])
all_step_ratios = np.squeeze(mdat['step_ratios'])
chain_length = disc.check_nums() / num_chains
# reshape if parallel
if comm.size > 1:
temp_input = np.reshape(disc._input_sample_set.\
get_values(), (num_chains, chain_length,
-1), 'F')
temp_output = np.reshape(disc._output_sample_set.\
get_values(), (num_chains, chain_length,
-1), 'F')
all_step_ratios = np.reshape(all_step_ratios,
(num_chains, chain_length), 'F')
# SPLIT DATA IF NECESSARY
if comm.size > 1 and (hot_start == 2 or (hot_start == 1 and \
len(mdat_files) != comm.size)):
# Use split to split along num_chains and set *._values_local
disc._input_sample_set.set_values_local(np.reshape(np.split(\
temp_input, comm.size, 0)[comm.rank],
(num_chains_pproc*chain_length, -1), 'F'))
disc._output_sample_set.set_values_local(np.reshape(np.split(\
temp_output, comm.size, 0)[comm.rank],
(num_chains_pproc*chain_length, -1), 'F'))
all_step_ratios = np.reshape(
np.split(all_step_ratios, comm.size, 0)[comm.rank],
(num_chains_pproc * chain_length, ), 'F')
kern_old = np.reshape(
np.split(kern_old, comm.size, 0)[comm.rank], (num_chains_pproc, ),
'F')
else:
all_step_ratios = np.reshape(all_step_ratios, (-1, ), 'F')
print chain_length * num_chains, chain_length, lb_model
new_sampler = sampler(chain_length * num_chains, chain_length, lb_model)
return (new_sampler, disc, all_step_ratios, kern_old)
def generalized_chains(self, param_min, param_max, t_set, kern,
savefile, initial_sample_type="random", criterion='center',
hot_start=0):
"""
Basic adaptive sampling algorithm using generalized chains.
:param string initial_sample_type: type of initial sample random (or r),
latin hypercube(lhs), or space-filling curve(TBD)
:param param_min: minimum value for each parameter dimension
:type param_min: :class:`numpy.ndarray` (ndim,)
:param param_max: maximum value for each parameter dimension
:type param_max: :class:`numpy.ndarray` (ndim,)
:param t_set: method for creating new parameter steps using
given a step size based on the paramter domain size
:type t_set: :class:`bet.sampling.adaptiveSampling.transition_set`
:param kern: functional that acts on the data used to
determine the proposed change to the ``step_size``
:type kernel: :class:~`bet.sampling.adaptiveSampling.kernel` object.
:param string savefile: filename to save samples and data
:param int hot_start: Flag whether or not hot start the sampling
chains from a previous set of chains. Note that ``num_chains`` must
be the same, but ``num_chains_pproc`` need not be the same. 0 -
cold start, 1 - hot start from uncompleted run, 2 - hot
start from finished run
:param string criterion: latin hypercube criterion see
`PyDOE <http://pythonhosted.org/pyDOE/randomized.html>`_
:rtype: tuple
:returns: (``parameter_samples``, ``data_samples``,
``all_step_ratios``) where ``parameter_samples`` is np.ndarray of
shape (num_samples, ndim), ``data_samples`` is np.ndarray of shape
(num_samples, mdim), and ``all_step_ratios`` is np.ndarray of shape
(num_chains, chain_length)
"""
if comm.size > 1:
psavefile = os.path.join(os.path.dirname(savefile),
"proc{}_{}".format(comm.rank, os.path.basename(savefile)))
# Initialize Nx1 vector Step_size = something reasonable (based on size
# of domain and transition set type)
# Calculate domain size
param_left = np.repeat([param_min], self.num_chains_pproc, 0)
param_right = np.repeat([param_max], self.num_chains_pproc, 0)
param_width = param_right - param_left
# Calculate step_size
max_ratio = t_set.max_ratio
min_ratio = t_set.min_ratio
if not hot_start:
step_ratio = t_set.init_ratio*np.ones(self.num_chains_pproc)
# Initiative first batch of N samples (maybe taken from latin
# hypercube/space-filling curve to fully explore parameter space -
# not necessarily random). Call these Samples_old.
(samples_old, data_old) = super(sampler, self).random_samples(
initial_sample_type, param_min, param_max, savefile,
self.num_chains, criterion)
self.num_samples = self.chain_length * self.num_chains
comm.Barrier()
# now split it all up
if comm.size > 1:
MYsamples_old = np.empty((np.shape(samples_old)[0]/comm.size,
np.shape(samples_old)[1]))
comm.Scatter([samples_old, MPI.DOUBLE], [MYsamples_old,
MPI.DOUBLE])
MYdata_old = np.empty((np.shape(data_old)[0]/comm.size,
np.shape(data_old)[1]))
comm.Scatter([data_old, MPI.DOUBLE], [MYdata_old, MPI.DOUBLE])
else:
MYsamples_old = np.copy(samples_old)
MYdata_old = np.copy(data_old)
samples = MYsamples_old
data = MYdata_old
all_step_ratios = step_ratio
(kern_old, proposal) = kern.delta_step(MYdata_old, None)
start_ind = 1
if hot_start:
# LOAD FILES
if hot_start == 1: # HOT START FROM PARTIAL RUN
if comm.rank == 0:
print "HOT START from partial run"
# Find and open save files
save_dir = os.path.dirname(savefile)
base_name = os.path.dirname(savefile)
mdat_files = glob.glob(os.path.join(save_dir,
"proc*_{}".format(base_name)))
if len(mdat_files) == 0:
print "HOT START using serial file"
mdat = sio.loadmat(savefile)
samples = mdat['samples']
data = mdat['data']
kern_old = np.squeeze(mdat['kern_old'])
all_step_ratios = np.squeeze(mdat['step_ratios'])
chain_length = samples.shape[0]/self.num_chains
if all_step_ratios.shape == (self.num_chains,
chain_length):
print "Serial file, from completed run updating hot_start"
hot_start = 2
# reshape if parallel
if comm.size > 1:
samples = np.reshape(samples, (self.num_chains,
chain_length, -1), 'F')
data = np.reshape(data, (self.num_chains,
chain_length, -1), 'F')
all_step_ratios = np.reshape(all_step_ratios,
(self.num_chains, -1), 'F')
elif hot_start == 1 and len(mdat_files) == comm.size:
print "HOT START using parallel files (same nproc)"
# if the number of processors is the same then set mdat to
# be the one with the matching processor number (doesn't
# really matter)
mdat = sio.loadmat(mdat_files[comm.rank])
samples = mdat['samples']
data = mdat['data']
kern_old = np.squeeze(mdat['kern_old'])
all_step_ratios = np.squeeze(mdat['step_ratios'])
elif hot_start == 1 and len(mdat_files) != comm.size:
print "HOT START using parallel files (diff nproc)"
# Determine how many processors the previous data used
# otherwise gather the data from mdat and then scatter
# among the processors and update mdat
mdat_files_local = comm.scatter(mdat_files)
mdat_local = [sio.loadmat(m) for m in mdat_files_local]
mdat_list = comm.allgather(mdat_local)
mdat_global = []
# instead of a list of lists, create a list of mdat
for mlist in mdat_list:
mdat_global.extend(mlist)
# get num_proc and num_chains_pproc for previous run
old_num_proc = max((len(mdat_list), 1))
old_num_chains_pproc = self.num_chains/old_num_proc
# get batch size and/or number of dimensions
chain_length = mdat_global[0]['samples'].shape[0]/\
old_num_chains_pproc
# create lists of local data
samples = []
data = []
all_step_ratios = []
kern_old = []
# RESHAPE old_num_chains_pproc, chain_length(or batch), dim
for mdat in mdat_global:
samples.append(np.reshape(mdat['samples'],
(old_num_chains_pproc, chain_length, -1), 'F'))
data.append(np.reshape(mdat['data'],
(old_num_chains_pproc, chain_length, -1), 'F'))
all_step_ratios.append(np.reshape(mdat['step_ratios'],
(old_num_chains_pproc, chain_length, -1), 'F'))
kern_old.append(np.reshape(mdat['kern_old'],
(old_num_chains_pproc,), 'F'))
# turn into arrays
samples = np.concatenate(samples)
data = np.concatenate(data)
all_step_ratios = np.concatenate(all_step_ratios)
kern_old = np.concatenate(kern_old)
if hot_start == 2: # HOT START FROM COMPLETED RUN:
if comm.rank == 0:
print "HOT START from completed run"
mdat = sio.loadmat(savefile)
samples = mdat['samples']
data = mdat['data']
kern_old = np.squeeze(mdat['kern_old'])
all_step_ratios = np.squeeze(mdat['step_ratios'])
chain_length = samples.shape[0]/self.num_chains
mdat_files = []
# reshape if parallel
if comm.size > 1:
samples = np.reshape(samples, (self.num_chains,
chain_length, -1), 'F')
data = np.reshape(data, (self.num_chains,
chain_length, -1), 'F')
all_step_ratios = np.reshape(all_step_ratios,
(self.num_chains, chain_length), 'F')
# SPLIT DATA IF NECESSARY
if comm.size > 1 and (hot_start == 2 or (hot_start == 1 and \
len(mdat_files) != comm.size)):
# Use split to split along num_chains
samples = np.reshape(np.split(samples, comm.size,
0)[comm.rank], (self.num_chains_pproc*chain_length, -1),
'F')
data = np.reshape(np.split(data, comm.size, 0)[comm.rank],
(self.num_chains_pproc*chain_length, -1), 'F')
all_step_ratios = np.reshape(np.split(all_step_ratios,
comm.size, 0)[comm.rank],
(self.num_chains_pproc*chain_length,), 'F')
kern_old = np.reshape(np.split(kern_old, comm.size,
0)[comm.rank], (self.num_chains_pproc,), 'F')
else:
all_step_ratios = np.reshape(all_step_ratios, (-1,), 'F')
# Set samples, data, all_step_ratios, mdat, step_ratio,
# MYsamples_old, and kern_old accordingly
step_ratio = all_step_ratios[-self.num_chains_pproc:]
MYsamples_old = samples[-self.num_chains_pproc:, :]
# Determine how many batches have been run
start_ind = samples.shape[0]/self.num_chains_pproc
mdat = dict()
self.update_mdict(mdat)
for batch in xrange(start_ind, self.chain_length):
# For each of N samples_old, create N new parameter samples using
# transition set and step_ratio. Call these samples samples_new.
samples_new = t_set.step(step_ratio, param_width,
param_left, param_right, MYsamples_old)
# Solve the model for the samples_new.
data_new = self.lb_model(samples_new)
# Make some decision about changing step_size(k). There are
# multiple ways to do this.
# Determine step size
(kern_old, proposal) = kern.delta_step(data_new, kern_old)
step_ratio = proposal*step_ratio
# Is the ratio greater than max?
step_ratio[step_ratio > max_ratio] = max_ratio
# Is the ratio less than min?
step_ratio[step_ratio < min_ratio] = min_ratio
# Save and export concatentated arrays
if self.chain_length < 4:
pass
elif comm.rank == 0 and (batch+1)%(self.chain_length/4) == 0:
print "Current chain length: "+\
str(batch+1)+"/"+str(self.chain_length)
samples = np.concatenate((samples, samples_new))
data = np.concatenate((data, data_new))
all_step_ratios = np.concatenate((all_step_ratios, step_ratio))
mdat['step_ratios'] = all_step_ratios
mdat['samples'] = samples
mdat['data'] = data
mdat['kern_old'] = kern_old
if comm.size > 1:
super(sampler, self).save(mdat, psavefile)
else:
super(sampler, self).save(mdat, savefile)
MYsamples_old = samples_new
# collect everything
MYsamples = np.copy(samples)
MYdata = np.copy(data)
MYall_step_ratios = np.copy(all_step_ratios)
# ``parameter_samples`` is np.ndarray of shape (num_samples, ndim)
samples = util.get_global_values(MYsamples,
shape=(self.num_samples, np.shape(MYsamples)[1]))
# and ``data_samples`` is np.ndarray of shape (num_samples, mdim)
data = util.get_global_values(MYdata, shape=(self.num_samples,
np.shape(MYdata)[1]))
# ``all_step_ratios`` is np.ndarray of shape (num_chains,
# chain_length)
all_step_ratios = util.get_global_values(MYall_step_ratios,
shape=(self.num_samples,))
all_step_ratios = np.reshape(all_step_ratios, (self.num_chains,
self.chain_length), 'F')
# save everything
mdat['step_ratios'] = all_step_ratios
mdat['samples'] = samples
mdat['data'] = data
mdat['kern_old'] = util.get_global_values(kern_old,
shape=(self.num_chains,))
super(sampler, self).save(mdat, savefile)
return (samples, data, all_step_ratios)
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)
