Source code for openmdao.core.system

""" Base class for all systems in OpenMDAO."""

import sys
import os
from fnmatch import fnmatch
from itertools import chain
import warnings

from six import string_types, iteritems, itervalues, iterkeys

import numpy as np

from openmdao.core.mpi_wrap import MPI
from openmdao.util.options import OptionsDictionary
from collections import OrderedDict
from openmdao.core.vec_wrapper import VecWrapper
from openmdao.core.vec_wrapper import _PlaceholderVecWrapper
from openmdao.util.type_util import real_types

trace = os.environ.get('OPENMDAO_TRACE')
if trace:  # pragma: no cover
    from openmdao.core.mpi_wrap import debug

class _SysData(object):
    """A container for System level data that is shared with
    VecWrappers in this System.
    """
    def __init__(self, pathname):
        self.pathname = pathname
        self._to_prom_name = {}
        self._to_top_prom_name = {}

[docs]class System(object): """ Base class for systems in OpenMDAO. When building models, user should inherit from `Group` or `Component` """ def __init__(self): self.name = '' self.pathname = '' self._subsystems = OrderedDict() self._params_dict = OrderedDict() self._unknowns_dict = OrderedDict() # specify which variables are promoted up to the parent. Wildcards # are allowed. self._promotes = () self.comm = None # create placeholders for all of the vectors self.unknowns = _PlaceholderVecWrapper('unknowns') self.resids = _PlaceholderVecWrapper('resids') self.params = _PlaceholderVecWrapper('params') self.dunknowns = _PlaceholderVecWrapper('dunknowns') self.dresids = _PlaceholderVecWrapper('dresids') opt = self.fd_options = OptionsDictionary() opt.add_option('force_fd', False, desc="Set to True to finite difference this system.") opt.add_option('form', 'forward', values=['forward', 'backward', 'central', 'complex_step'], desc="Finite difference mode. (forward, backward, central) " "You can also set to 'complex_step' to peform the complex " "step method if your components support it.") opt.add_option("step_size", 1.0e-6, desc="Default finite difference stepsize") opt.add_option("step_type", 'absolute', values=['absolute', 'relative'], desc='Set to absolute, relative') self._impl = None self._num_par_fds = 1 # this will be >1 for ParallelFDGroup self._par_fd_id = 0 # for ParallelFDGroup, this will be >= 0 and # <= the number of parallel FDs self._reset() # initialize some attrs that are set during setup def _reset(self): """This is called at the beginning of the problem setup.""" self.pathname = '' self._sysdata = _SysData('') # dicts of vectors used for parallel solution of multiple RHS self.dumat = {} self.dpmat = {} self.drmat = {} self._local_subsystems = [] self._relevance = None self._fd_params = None def __getitem__(self, name): """ Return the variable of the given name from this system. Args ---- name : str The name of the variable. Returns ------- value The unflattened value of the given variable. """ msg = "Variable '%s' must be accessed from a containing Group" raise RuntimeError(msg % name) def _promoted(self, name): """Determine if the given variable name is being promoted from this `System`. Args ---- name : str The name of a variable, relative to this `System`. Returns ------- bool True if the named variable is being promoted from this `System`. Raises ------ TypeError if the promoted variable specifications are not in a valid format """ if isinstance(self._promotes, string_types): raise TypeError("'%s' promotes must be specified as a list, " "tuple or other iterator of strings, but '%s' was specified" % (self.name, self._promotes)) for prom in self._promotes: if fnmatch(name, prom): for meta in chain(itervalues(self._params_dict), itervalues(self._unknowns_dict)): if name == meta.get('promoted_name'): return True return False
[docs] def check_setup(self, out_stream=sys.stdout): """Write a report to the given stream indicating any potential problems found with the current configuration of this ``System``. Args ---- out_stream : a file-like object, optional Stream where report will be written. """ pass
def _check_promotes(self): """Check that the `System`s promotes are valid. Raise an Exception if there are any promotes that do not match at least one variable in the `System`. Raises ------ TypeError if the promoted variable specifications are not in a valid format RuntimeError if a promoted variable specification does not match any variables """ if isinstance(self._promotes, string_types): raise TypeError("'%s' promotes must be specified as a list, " "tuple or other iterator of strings, but '%s' was specified" % (self.name, self._promotes)) for prom in self._promotes: for name, meta in chain(iteritems(self._params_dict), iteritems(self._unknowns_dict)): if 'promoted_name' in meta: pname = meta['promoted_name'] else: pname = name if fnmatch(pname, prom): break else: msg = "'%s' promotes '%s' but has no variables matching that specification" raise RuntimeError(msg % (self.pathname, prom))
[docs] def subsystems(self, local=False, recurse=False, include_self=False): """ Returns an iterator over subsystems. For `System`, this is an empty list. Args ---- local : bool, optional If True, only return those `Components` that are local. Default is False. recurse : bool, optional If True, return all `Components` in the system tree, subject to the value of the local arg. Default is False. typ : type, optional If a class is specified here, only those subsystems that are instances of that type will be returned. Default type is `System`. include_self : bool, optional If True, yield self before iterating over subsystems, assuming type of self is appropriate. Default is False. Returns ------- iterator Iterator over subsystems. """ if include_self: yield self
def _init_sys_data(self, parent_path, probdata): """Set the absolute pathname of each `System` in the tree. Parameter --------- parent_path : str The pathname of the parent `System`, which is to be prepended to the name of this child `System`. probdata : `_ProbData` Problem level data container. """ self._reset() if parent_path: self.pathname = '.'.join((parent_path, self.name)) else: self.pathname = self.name self._sysdata = _SysData(self.pathname) self._probdata = probdata
[docs] def solve_linear(self, dumat, drmat, vois, mode=None): """ Single linear solution applied to whatever input is sitting in the rhs vector. Args ---- dumat : dict of `VecWrappers` In forward mode, each `VecWrapper` contains the incoming vector for the states. There is one vector per quantity of interest for this problem. In reverse mode, it contains the outgoing vector for the states. (du) drmat : `dict of VecWrappers` `VecWrapper` containing either the outgoing result in forward mode or the incoming vector in reverse mode. There is one vector per quantity of interest for this problem. (dr) vois : list of strings List of all quantities of interest to key into the mats. mode : string Derivative mode, can be 'fwd' or 'rev', but generally should be called without mode so that the user can set the mode in this system's ln_solver.options. """ pass
[docs] def is_active(self): """ Returns ------- bool If running under MPI, returns True if this `System` has a valid communicator. Always returns True if not running under MPI. """ return MPI is None or not (self.comm is None or self.comm == MPI.COMM_NULL)
[docs] def get_req_procs(self): """ Returns ------- tuple A tuple of the form (min_procs, max_procs), indicating the min and max processors usable by this `System`. """ return (1, 1)
def _setup_communicators(self, comm): """ Assign communicator to this `System` and all of its subsystems. Args ---- comm : an MPI communicator (real or fake) The communicator being offered by the parent system. """ minp, maxp = self.get_req_procs() if MPI and comm is not None and comm != MPI.COMM_NULL and comm.size < minp: raise RuntimeError("%s needs %d MPI processes, but was given only %d." % (self.pathname, minp, comm.size)) self.comm = comm def _set_vars_as_remote(self): """ Set 'remote' attribute in metadata of all variables for this subsystem. """ for meta in itervalues(self._params_dict): meta['remote'] = True for meta in itervalues(self._unknowns_dict): meta['remote'] = True
[docs] def fd_jacobian(self, params, unknowns, resids, total_derivs=False, fd_params=None, fd_unknowns=None, poi_indices=None, qoi_indices=None): """Finite difference across all unknowns in this system w.r.t. all incoming params. Args ---- params : `VecWrapper` `VecWrapper` containing parameters. (p) unknowns : `VecWrapper` `VecWrapper` containing outputs and states. (u) resids : `VecWrapper` `VecWrapper` containing residuals. (r) total_derivs : bool, optional Set to true to calculate total derivatives. Otherwise, partial derivatives are returned. fd_params : list of strings, optional List of parameter name strings with respect to which derivatives are desired. This is used by problem to limit the derivatives that are taken. fd_unknowns : list of strings, optional List of output or state name strings for derivatives to be calculated. This is used by problem to limit the derivatives that are taken. poi_indices: dict of list of integers, optional This is a dict that contains the index values for each parameter of interest, so that we only finite difference those indices. qoi_indices: dict of list of integers, optional This is a dict that contains the index values for each quantity of interest, so that the finite difference is returned only for those indices. Returns ------- dict Dictionary whose keys are tuples of the form ('unknown', 'param') and whose values are ndarrays containing the derivative for that tuple pair. """ # Params and Unknowns that we provide at this level. if fd_params is None: fd_params = self._get_fd_params() if fd_unknowns is None: fd_unknowns = self._get_fd_unknowns() # Use settings in the system dict unless variables override. step_size = self.fd_options.get('step_size', 1.0e-6) form = self.fd_options.get('form', 'forward') step_type = self.fd_options.get('step_type', 'relative') jac = {} cache2 = None # Prepare for calculating partial derivatives or total derivatives if total_derivs: run_model = self.solve_nonlinear resultvec = unknowns states = () else: run_model = self.apply_nonlinear resultvec = resids states = self.states cache1 = resultvec.vec.copy() gather_jac = False fd_count = -1 # if doing parallel FD, we need to save results during calculation # and then pass them around. fd_cols stores the # column data keyed by (uname, pname, col_id). fd_cols = {} # Compute gradient for this param or state. for p_name in chain(fd_params, states): # If our input is connected to a IndepVarComp, then we need to twiddle # the unknowns vector instead of the params vector. src = self.connections.get(p_name) if src is not None: param_src = src[0] # just the name # Have to convert to promoted name to key into unknowns if param_src not in self.unknowns: param_src = self.unknowns.get_promoted_varname(param_src) target_input = unknowns.flat[param_src] else: # Cases where the IndepVarComp is somewhere above us. if p_name in states: inputs = unknowns else: inputs = params target_input = inputs.flat[p_name] mydict = {} if p_name in self._to_abs_pnames: for meta in itervalues(self._params_dict): if meta['promoted_name'] == p_name: mydict = meta break # Local settings for this var trump all fdstep = mydict.get('step_size', step_size) fdtype = mydict.get('step_type', step_type) fdform = mydict.get('form', form) # Size our Inputs if poi_indices and param_src in poi_indices: p_idxs = poi_indices[param_src] p_size = len(p_idxs) else: p_size = np.size(target_input) p_idxs = range(p_size) # Size our Outputs for u_name in fd_unknowns: if qoi_indices and u_name in qoi_indices: u_size = len(qoi_indices[u_name]) else: u_size = np.size(unknowns[u_name]) jac[u_name, p_name] = np.zeros((u_size, p_size)) # if a given param isn't present in this process, we need # to still run the model once for each entry in that param # in order to stay in sync with the other processes. if p_size == 0: gather_jac = True p_idxs = range(self._params_dict[p_name]['size']) # Finite Difference each index in array for col, idx in enumerate(p_idxs): fd_count += 1 # skip the current index if its done by some other # parallel fd proc if fd_count % self._num_par_fds == self._par_fd_id: if p_size == 0: run_model(params, unknowns, resids) continue # Relative or Absolute step size if fdtype == 'relative': step = target_input[idx] * fdstep if step < fdstep: step = fdstep else: step = fdstep if fdform == 'forward': target_input[idx] += step run_model(params, unknowns, resids) target_input[idx] -= step # delta resid is delta unknown resultvec.vec[:] -= cache1 resultvec.vec[:] *= (1.0/step) elif fdform == 'backward': target_input[idx] -= step run_model(params, unknowns, resids) target_input[idx] += step # delta resid is delta unknown resultvec.vec[:] -= cache1 resultvec.vec[:] *= (-1.0/step) elif fdform == 'central': target_input[idx] += step run_model(params, unknowns, resids) cache2 = resultvec.vec.copy() target_input[idx] -= step resultvec.vec[:] = cache1 target_input[idx] -= step run_model(params, unknowns, resids) # central difference formula resultvec.vec[:] -= cache2 resultvec.vec[:] *= (-0.5/step) target_input[idx] += step for u_name in fd_unknowns: if qoi_indices and u_name in qoi_indices: result = resultvec.flat[u_name][qoi_indices[u_name]] else: result = resultvec.flat[u_name] jac[u_name, p_name][:, col] = result if self._num_par_fds > 1: # pragma: no cover fd_cols[(u_name, p_name, col)] = \ jac[u_name, p_name][:, col] # Restore old residual resultvec.vec[:] = cache1 if self._num_par_fds > 1: if trace: # pragma: no cover debug("%s: allgathering parallel FD columns" % self.pathname) jacinfos = self._full_comm.allgather(fd_cols) for rank, jacinfo in enumerate(jacinfos): if rank == self._full_comm.rank: continue for key, val in iteritems(jacinfo): if key not in fd_cols: uname, pname, col = key jac[uname, pname][:, col] = val fd_cols[(uname, pname, col)] = val # to avoid setting dups elif MPI and gather_jac: jac = self.get_combined_jac(jac) return jac
def _sys_apply_linear(self, mode, ls_inputs=None, vois=(None,), gs_outputs=None): """ Entry point method for all parent classes to access the apply_linear method. This method handles the functionality for self-fd, or otherwise passes the call down to the apply_linear method. Args ---- mode : string Derivative mode, can be 'fwd' or 'rev'. vois: list of strings List of all quantities of interest to key into the mats. ls_inputs : dict We can only solve derivatives for the inputs the instigating system has access to. gs_outputs : dict, optional Linear Gauss-Siedel can limit the outputs when calling apply. """ force_fd = self.fd_options['force_fd'] states = self.states is_relevant = self._relevance.is_relevant_system fwd = mode == "fwd" for voi in vois: # don't call apply_linear if this system is irrelevant if not is_relevant(voi, self): continue dresids = self.drmat[voi] dunknowns = self.dumat[voi] dparams = self.dpmat[voi] gsouts = None if gs_outputs is None else gs_outputs[voi] # Linear GS imposes a stricter requirement on whether or not to run. abs_inputs = self._abs_inputs[voi] do_apply = ls_inputs[voi] is None or (abs_inputs and len(abs_inputs.intersection(ls_inputs[voi]))) if fwd: dresids.vec[:] = 0.0 if do_apply: dparams._apply_unit_derivatives() if force_fd: self._apply_linear_jac(self.params, self.unknowns, dparams, dunknowns, dresids, mode) else: self.apply_linear(self.params, self.unknowns, dparams, dunknowns, dresids, mode) dresids.vec *= -1.0 for var, val in iteritems(dunknowns.flat): # Skip all states if (gsouts is None or var in gsouts) and \ var not in states: dresids.flat[var] += val else: for val in itervalues(dparams.flat): val[:] = 0.0 for val in itervalues(dunknowns.flat): val[:] = 0.0 if do_apply: try: # Sign on the local Jacobian needs to be -1 before # we add in the fake residual. Since we can't modify # the 'du' vector at this point without stomping on the # previous component's contributions, we can multiply # our local 'arg' by -1, and then revert it afterwards. dresids.vec *= -1.0 if force_fd: self._apply_linear_jac(self.params, self.unknowns, dparams, dunknowns, dresids, mode) else: self.apply_linear(self.params, self.unknowns, dparams, dunknowns, dresids, mode) dresids.vec *= -1.0 finally: dparams._apply_unit_derivatives() for var, val in iteritems(dresids.flat): # Skip all states if (gsouts is None or var in gsouts) and \ var not in states: dunknowns.flat[var] += val def _sys_linearize(self, params, unknowns, resids, total_derivs=None): """ Entry point for all callers to cause linearization of system and all children of system Args ---- params : `VecWrapper` `VecWrapper` containing parameters. (p) unknowns : `VecWrapper` `VecWrapper` containing outputs and states. (u) resids : `VecWrapper` `VecWrapper` containing residuals. (r) total_derivs: bool flag indicating if total or partial derivatives are being forced. None allows the system to choose whats appropriate for itself """ if self.fd_options['force_fd']: #force_fd should compute semi-totals across all children, # unless total_derivs=False is specifically requested if self._local_subsystems and total_derivs is None: self._jacobian_cache = self.fd_jacobian(params, unknowns, resids, total_derivs=True) else: # Component can request to use complex step. if self.fd_options['form'] == 'complex_step': fd_func = self.complex_step_jacobian else: fd_func = self.fd_jacobian self._jacobian_cache = fd_func(params, unknowns, resids, total_derivs=False) else: try: linearize = self.jacobian except AttributeError: linearize = self.linearize else: warnings.simplefilter('always', DeprecationWarning) warnings.warn("%s: The 'jacobian' method is deprecated. Please " "rename 'jacobian' to 'linearize'." % self.pathname, DeprecationWarning,stacklevel=2) warnings.simplefilter('ignore', DeprecationWarning) self._jacobian_cache = linearize(params, unknowns, resids) if self._jacobian_cache is not None: jc = self._jacobian_cache for key, J in iteritems(jc): if isinstance(J, real_types): jc[key] = np.array([[J]]) shape = jc[key].shape if len(shape) < 2: jc[key] = jc[key].reshape((shape[0], 1)) return self._jacobian_cache def _apply_linear_jac(self, params, unknowns, dparams, dunknowns, dresids, mode): """ See apply_linear. This method allows the framework to override any derivative specification in any `Component` or `Group` to perform finite difference.""" if not self._jacobian_cache: msg = ("No derivatives defined for Component '{name}'") msg = msg.format(name=self.name) raise ValueError(msg) isvw = isinstance(dresids, VecWrapper) fwd = mode == 'fwd' try: states = self.states except AttributeError: # handle component unit test where setup has not been performed # TODO: should we force all component unit tests to use a Problem test harness? states = set([p for u,p in iterkeys(self._jacobian_cache) if p not in dparams]) for (unknown, param), J in iteritems(self._jacobian_cache): if param in states: arg_vec = dunknowns else: arg_vec = dparams # Vectors are flipped during adjoint try: if isvw: if fwd: vec = dresids._flat(unknown) vec += J.dot(arg_vec._flat(param)) else: shape = arg_vec._vardict[param]['shape'] arg_vec[param] += J.T.dot(dresids._flat(unknown)).reshape(shape) else: # plain dicts were passed in for unit testing... if fwd: vec = dresids[unknown] vec += J.dot(arg_vec[param].flat).reshape(vec.shape) else: shape = arg_vec[param].shape arg_vec[param] += J.T.dot(dresids[unknown].flat).reshape(shape) except KeyError: continue # either didn't find param in dparams/dunknowns or # didn't find unknown in dresids def _create_views(self, top_unknowns, parent, my_params, voi=None): """ A manager of the data transfer of a possibly distributed collection of variables. The variables are based on views into an existing `VecWrapper`. Args ---- top_unknowns : `VecWrapper` The `Problem` level unknowns `VecWrapper`. parent : `System` The `System` which provides the `VecWrapper` on which to create views. my_params : list List of pathnames for parameters that this `Group` is responsible for propagating. relevance : `Relevance` Object containing relevance info for each variable of interest. voi : str The name of a variable of interest. """ comm = self.comm params_dict = self._params_dict relevance = self._relevance # map promoted name in parent to corresponding promoted name in this view umap = self._relname_map if voi is None: self.unknowns = parent.unknowns.get_view(self, comm, umap) self.states = set((n for n,m in iteritems(self.unknowns) if m.get('state'))) self.resids = parent.resids.get_view(self, comm, umap) self.params = parent._impl.create_tgt_vecwrapper(self._sysdata, comm) self.params.setup(parent.params, params_dict, top_unknowns, my_params, self.connections, relevance=relevance, store_byobjs=True) self.dumat[voi] = parent.dumat[voi].get_view(self, comm, umap) self.drmat[voi] = parent.drmat[voi].get_view(self, comm, umap) self.dpmat[voi] = parent._impl.create_tgt_vecwrapper(self._sysdata, comm) self.dpmat[voi].setup(parent.dpmat[voi], params_dict, top_unknowns, my_params, self.connections, relevance=relevance, var_of_interest=voi, shared_vec=self._shared_dp_vec[self._shared_p_offsets[voi]:]) def _setup_gs_outputs(self, vois): self.gs_outputs = { 'fwd': {}, 'rev': {}} dumat = self.dumat gso = self.gs_outputs['fwd'] for sub in self._local_subsystems: gso[sub.name] = outs = {} for voi in vois: outs[voi] = set([x for x in dumat[voi] if sub.dumat and x not in sub.dumat[voi]]) gso = self.gs_outputs['rev'] for sub in reversed(self._local_subsystems): gso[sub.name] = outs = {} for voi in vois: outs[voi] = set([x for x in dumat[voi] if not sub.dumat or (sub.dumat and x not in sub.dumat[voi])])
[docs] def get_combined_jac(self, J): """ Take a J dict that's distributed, i.e., has different values across different MPI processes, and return a dict that contains all of the values from all of the processes. If values are duplicated, use the value from the lowest rank process. Note that J has a nested dict structure. Args ---- J : `dict` Local Jacobian Returns ------- `dict` Local gathered Jacobian """ if not self.is_active(): return J comm = self.comm iproc = comm.rank # TODO: calculate dist_need_tups and dist_has_tups once # and cache it instead of doing every time. need_tups = [] has_tups = [] # Gather a list of local tuples for J. for (output, param), value in iteritems(J): if value.size == 0: need_tups.append((output, param)) else: has_tups.append((output, param)) if trace: # pragma: no cover debug("%s: allgather of needed tups" % self.pathname) dist_need_tups = comm.allgather(need_tups) needed_set = set() for need_tups in dist_need_tups: needed_set.update(need_tups) if not needed_set: return J # nobody needs any J entries if trace: # pragma: no cover debug("%s: allgather of has_tups" % self.pathname) dist_has_tups = comm.allgather(has_tups) found = set() owned_vals = [] for rank, tups in enumerate(dist_has_tups): for tup in tups: if tup in needed_set and not tup in found: found.add(tup) if rank == iproc: owned_vals.append((tup, J[tup])) if trace: # pragma: no cover debug("%s: allgather of owned vals" % self.pathname) dist_vals = comm.allgather(owned_vals) for rank, vals in enumerate(dist_vals): if rank != iproc: for (output, param), value in vals: J[output, param] = value return J
def _get_var_pathname(self, name): if self.pathname: return '.'.join((self.pathname, name)) return name
[docs] def generate_docstring(self): """ Generates a numpy-style docstring for a user-created System class. Returns ------- docstring : str string that contains a basic numpy docstring. """ #start the docstring off docstring = ' \"\"\"\n' if self._params_dict or self._unknowns_dict: docstring += '\n Params\n ----------\n' if self._params_dict: for key, value in self._params_dict.items(): #docstring += type(value).__name__ docstring += " " + key + ": param ({" #get the values out in order dictItemCount = len(value) dictPosition = 1 for k in sorted(value): docstring += "'" +k+ "'" + ": " + str(value[k]) #don't want a trailing comma if (dictPosition != dictItemCount): docstring += ", " dictPosition += 1 docstring += "})\n" if self._unknowns_dict: for key, value in self._unknowns_dict.items(): docstring += " " + key + " : unknown ({" dictItemCount = len(value) dictPosition = 1 for k in sorted(value): docstring += "'" +k+ "'" + ": " + str(value[k]) if (dictPosition != dictItemCount): docstring += ", " dictPosition += 1 docstring += "})\n" #Put options into docstring firstTime = 1 #for py3.4, items from vars must come out in same order. v = OrderedDict(sorted(vars(self).items())) for key, value in v.items(): if type(value)==OptionsDictionary: if firstTime: #start of Options docstring docstring += '\n Options\n -------\n' firstTime = 0 for (name, val) in sorted(value.items()): docstring += " " + key + "['" docstring += name + "']" docstring += " : " + type(val).__name__ docstring += "(" if type(val).__name__ == 'str': docstring += "'" docstring += str(val) if type(val).__name__ == 'str': docstring += "'" docstring += ")\n" desc = value._options[name]['desc'] if(desc): docstring += " " + desc + "\n" #finish up docstring docstring += '\n \"\"\"\n' return docstring
def _get_shared_vec_info(self, vdict, my_params=None): # determine the size of the largest grouping of parallel subvecs and the # offsets within those vecs for each voi in a parallel set. # We should never need more memory than the largest sized collection of parallel # vecs. metas = [m for m in itervalues(vdict) if not m.get('pass_by_obj')] # for params, we only include 'owned' vars in the vector if my_params is not None: metas = [m for m in metas if m['pathname'] in my_params] full_size = sum([m['size'] for m in metas]) # 'None' vecs are this size max_size = full_size offsets = { None: 0 } # no parallel rhs vecs, so biggest one will just be the one containing all # vars. if not self._probdata.top_lin_gs: return max_size, offsets relevance = self._relevance for vois in relevance.groups: vec_size = 0 for voi in vois: sz = sum([m['size'] for m in metas if m['pathname'] in vdict and relevance.is_relevant(voi, m['top_promoted_name'])]) offsets[voi] = vec_size vec_size += sz if vec_size > max_size: max_size = vec_size return max_size, offsets
def _iter_J_nested(J): for output, subdict in iteritems(J): for param, value in iteritems(subdict): yield (output, param), value