text: """Define the Component class."""
  
  from __future__ import division
  
  from collections import OrderedDict, Iterable, Counter
  from itertools import product
  from six import string_types, iteritems
  
  import numpy as np
  from numpy import ndarray, isscalar, atleast_1d, atleast_2d, promote_types
  from scipy.sparse import issparse
  
  from openmdao.approximation_schemes.complex_step import ComplexStep, DEFAULT_CS_OPTIONS
  from openmdao.approximation_schemes.finite_difference import FiniteDifference, DEFAULT_FD_OPTIONS
  from openmdao.core.system import System
  from openmdao.jacobians.assembled_jacobian import SUBJAC_META_DEFAULTS
  from openmdao.jacobians.dictionary_jacobian import DictionaryJacobian
  from openmdao.utils.units import valid_units
  from openmdao.utils.general_utils import format_as_float_or_array, ensure_compatible, \
      warn_deprecation, find_matches, simple_warning
  from openmdao.vectors.vector import INT_DTYPE
  from openmdao.utils.name_maps import rel_key2abs_key, abs_key2rel_key
  from openmdao.utils.mpi import MPI
  
  
  # Suppored methods for derivatives
  _supported_methods = {'fd': (FiniteDifference, DEFAULT_FD_OPTIONS),
                        'cs': (ComplexStep, DEFAULT_CS_OPTIONS),
                        'exact': (None, {})}
  
  
  # the following metadata will be accessible for vars on all procs
  global_meta_names = {
      'input': ('units', 'shape', 'size', 'distributed'),
      'output': ('units', 'shape', 'size',
                 'ref', 'ref0', 'res_ref', 'distributed', 'lower', 'upper'),
  }
  
  
  def _valid_var_name(name):
      """
      Determine if the proposed name is a valid variable name.
  
      Parameters
      ----------
      name : str
          Proposed name.
  
      Returns
      -------
      bool
          True if the proposed name is a valid variable name, else False.
      """
      forbidden_chars = ['.', '*', '?', '!', '[', ']']
  
      return not any([True for character in forbidden_chars if character in name])
  
  
  class Component(System):
      """
      Base Component class; not to be directly instantiated.
  
      Attributes
      ----------
      _approx_schemes : OrderedDict
          A mapping of approximation types to the associated ApproximationScheme.
      _var_rel2meta : dict
          Dictionary mapping relative names to metadata.
          This is only needed while adding inputs and outputs. During setup, these are used to
          build the dictionaries of metadata.
      _static_var_rel2meta : dict
          Static version of above - stores data for variables added outside of setup.
      _var_rel_names : {'input': [str, ...], 'output': [str, ...]}
          List of relative names of owned variables existing on current proc.
          This is only needed while adding inputs and outputs. During setup, these are used to
          determine the list of absolute names.
      _static_var_rel_names : dict
          Static version of above - stores names of variables added outside of setup.
      _declared_partials : list
          Cached storage of user-declared partials.
      _approximated_partials : list
          Cached storage of user-declared approximations.
      _declared_partial_checks : list
          Cached storage of user-declared check partial options.
      """
  
      def __init__(self, **kwargs):
          """
          Initialize all attributes.
  
          Parameters
          ----------
          **kwargs : dict of keyword arguments
              available here and in all descendants of this system.
          """
          super(Component, self).__init__(**kwargs)
  
          self._approx_schemes = OrderedDict()
  
          self._var_rel_names = {'input': [], 'output': []}
          self._var_rel2meta = {}
  
          self._static_var_rel_names = {'input': [], 'output': []}
          self._static_var_rel2meta = {}
  
          self._declared_partials = []
          self._approximated_partials = []
          self._declared_partial_checks = []
  
      def _declare_options(self):
          """
          Declare options before kwargs are processed in the init method.
          """
          super(Component, self)._declare_options()
  
          self.options.declare('distributed', False,
                               desc='True if the component has variables that are distributed '
                                    'across multiple processes.')
  
      @property
      def distributed(self):
          """
          Provide 'distributed' property for backwards compatibility.
  
          Returns
          -------
          bool
              reference to the 'distributed' option.
          """
          warn_deprecation("The 'distributed' property provides backwards compatibility "
                           "with OpenMDAO <= 2.4.0 ; use the 'distributed' option instead.")
          return self.options['distributed']
  
      @distributed.setter
      def distributed(self, val):
          """
          Provide for setting of the 'distributed' property for backwards compatibility.
  
          Parameters
          ----------
          val : bool
              True if the component has variables that are distributed across multiple processes.
          """
          warn_deprecation("The 'distributed' property provides backwards compatibility "
                           "with OpenMDAO <= 2.4.0 ; use the 'distributed' option instead.")
          self.options['distributed'] = val
  
      def setup(self):
          """
          Declare inputs and outputs.
  
          Available attributes:
              name
              pathname
              comm
              options
          """
          pass
  
      def _setup_procs(self, pathname, comm, mode):
          """
          Execute first phase of the setup process.
  
          Distribute processors, assign pathnames, and call setup on the component.
  
          Parameters
          ----------
          pathname : str
              Global name of the system, including the path.
          comm : MPI.Comm or <FakeComm>
              MPI communicator object.
          mode : string
              Derivatives calculation mode, 'fwd' for forward, and 'rev' for
              reverse (adjoint). Default is 'rev'.
          """
          self.pathname = pathname
  
          orig_comm = comm
          if self._num_par_fd > 1:
              if comm.size > 1:
                  comm = self._setup_par_fd_procs(comm)
              elif not MPI:
                  msg = ("'%s': MPI is not active but num_par_fd = %d. No parallel finite difference "
                         "will be performed." % (self.pathname, self._num_par_fd))
                  simple_warning(msg)
  
          self.comm = comm
          self._mode = mode
          self._subsystems_proc_range = []
  
          # Clear out old variable information so that we can call setup on the component.
          self._var_rel_names = {'input': [], 'output': []}
          self._var_rel2meta = {}
          self._design_vars = OrderedDict()
          self._responses = OrderedDict()
  
          self._static_mode = False
          self._var_rel2meta.update(self._static_var_rel2meta)
          for type_ in ['input', 'output']:
              self._var_rel_names[type_].extend(self._static_var_rel_names[type_])
          self._design_vars.update(self._static_design_vars)
          self._responses.update(self._static_responses)
          self.setup()
  
          # check to make sure that if num_par_fd > 1 that this system is actually doing FD.
          # Unfortunately we have to do this check after system setup has been called because that's
          # when declare_partials generally happens, so we raise an exception here instead of just
          # resetting the value of num_par_fd (because the comm has already been split and possibly
          # used by the system setup).
          if self._num_par_fd > 1 and orig_comm.size > 1 and not (self._owns_approx_jac or
                                                                  self._approximated_partials):
              raise RuntimeError("'%s': num_par_fd is > 1 but no FD is active." % self.pathname)
  
          self._static_mode = True
  
          if self.options['distributed']:
              if self._distributed_vector_class is not None:
                  self._vector_class = self._distributed_vector_class
              else:
                  simple_warning("The 'distributed' option is set to True for Component %s, "
                                 "but there is no distributed vector implementation (MPI/PETSc) "
                                 "available. The default non-distributed vectors will be used."
                                 % pathname)
                  self._vector_class = self._local_vector_class
          else:
              self._vector_class = self._local_vector_class
  
      def _setup_var_data(self, recurse=True):
          """
          Compute the list of abs var names, abs/prom name maps, and metadata dictionaries.
  
          Parameters
          ----------
          recurse : bool
              Whether to call this method in subsystems.
          """
          global global_meta_names
          super(Component, self)._setup_var_data()
          allprocs_abs_names = self._var_allprocs_abs_names
          allprocs_prom2abs_list = self._var_allprocs_prom2abs_list
          abs2prom = self._var_abs2prom
          allprocs_abs2meta = self._var_allprocs_abs2meta
          abs2meta = self._var_abs2meta
  
          # Compute the prefix for turning rel/prom names into abs names
          prefix = self.pathname + '.' if self.pathname else ''
  
          for type_ in ['input', 'output']:
              for prom_name in self._var_rel_names[type_]:
                  abs_name = prefix + prom_name
                  metadata = self._var_rel2meta[prom_name]
  
                  # Compute allprocs_abs_names, abs_names
                  allprocs_abs_names[type_].append(abs_name)
  
                  # Compute allprocs_prom2abs_list, abs2prom
                  allprocs_prom2abs_list[type_][prom_name] = [abs_name]
                  abs2prom[type_][abs_name] = prom_name
  
                  # Compute allprocs_abs2meta
                  allprocs_abs2meta[abs_name] = {
                      meta_name: metadata[meta_name]
                      for meta_name in global_meta_names[type_]
                  }
  
                  # Compute abs2meta
                  abs2meta[abs_name] = metadata
  
              for prom_name, val in iteritems(self._var_discrete[type_]):
                  abs_name = prefix + prom_name
                  allprocs_prom2abs_list[type_][prom_name] = [abs_name]
                  self._var_allprocs_discrete[type_][abs_name] = val
  
          self._var_abs_names = self._var_allprocs_abs_names
          if self._var_discrete['input'] or self._var_discrete['output']:
              self._discrete_inputs = _DictValues(self._var_discrete['input'])
              self._discrete_outputs = _DictValues(self._var_discrete['output'])
          else:
              self._discrete_inputs = self._discrete_outputs = ()
  
      def _setup_var_sizes(self, recurse=True):
          """
          Compute the arrays of local variable sizes for all variables/procs on this system.
  
          Parameters
          ----------
          recurse : bool
              Whether to call this method in subsystems.
          """
          super(Component, self)._setup_var_sizes()
  
          iproc = self.comm.rank
          nproc = self.comm.size
  
          sizes = self._var_sizes
          abs2meta = self._var_abs2meta
  
          if self._use_derivatives:
              vec_names = self._lin_rel_vec_name_list
          else:
              vec_names = self._vec_names
  
          # Initialize empty arrays
          for vec_name in vec_names:
              # at component level, _var_allprocs_* is the same as var_* since all vars exist in all
              # procs for a given component, so we don't have to mess with figuring out what vars are
              # local.
              if self._use_derivatives:
                  relnames = self._var_allprocs_relevant_names[vec_name]
              else:
                  relnames = self._var_allprocs_abs_names
  
              sizes[vec_name] = {}
              for type_ in ('input', 'output'):
                  sizes[vec_name][type_] = sz = np.zeros((nproc, len(relnames[type_])), int)
  
                  # Compute _var_sizes
                  for idx, abs_name in enumerate(relnames[type_]):
                      sz[iproc, idx] = abs2meta[abs_name]['size']
  
          if nproc > 1:
              for vec_name in vec_names:
                  sizes = self._var_sizes[vec_name]
                  if self.options['distributed']:
                      for type_ in ['input', 'output']:
                          self.comm.Allgather(sizes[type_][iproc, :], sizes[type_])
                  else:
                      # if component isn't distributed, we don't need to allgather sizes since
                      # they'll all be the same.
                      for type_ in ['input', 'output']:
                          sizes[type_] = np.tile(sizes[type_][iproc], (nproc, 1))
  
          if self._use_derivatives:
              self._var_sizes['nonlinear'] = self._var_sizes['linear']
  
          self._setup_global_shapes()
  
      def _setup_partials(self, recurse=True):
          """
          Process all partials and approximations that the user declared.
  
          Parameters
          ----------
          recurse : bool
              Whether to call this method in subsystems.
          """
          self._subjacs_info = {}
          self._jacobian = DictionaryJacobian(system=self)
  
          for of, wrt, dependent, rows, cols, val in self._declared_partials:
              self._declare_partials(of, wrt, dependent=dependent, rows=rows, cols=cols, val=val)
  
          for of, wrt, method, kwargs in self._approximated_partials:
              self._approx_partials(of, wrt, method=method, **kwargs)
  
      def add_input(self, name, val=1.0, shape=None, src_indices=None, flat_src_indices=None,
                    units=None, desc=''):
          """
          Add an input variable to the component.
  
          Parameters
          ----------
          name : str
              name of the variable in this component's namespace.
          val : float or list or tuple or ndarray or Iterable
              The initial value of the variable being added in user-defined units.
              Default is 1.0.
          shape : int or tuple or list or None
              Shape of this variable, only required if src_indices not provided and
              val is not an array. Default is None.
          src_indices : int or list of ints or tuple of ints or int ndarray or Iterable or None
              The global indices of the source variable to transfer data from.
              A value of None implies this input depends on all entries of source.
              Default is None. The shapes of the target and src_indices must match,
              and form of the entries within is determined by the value of 'flat_src_indices'.
          flat_src_indices : bool
              If True, each entry of src_indices is assumed to be an index into the
              flattened source.  Otherwise each entry must be a tuple or list of size equal
              to the number of dimensions of the source.
          units : str or None
              Units in which this input variable will be provided to the component
              during execution. Default is None, which means it is unitless.
          desc : str
              description of the variable
  
          Returns
          -------
          dict
              metadata for added variable
          """
          if units == 'unitless':
              warn_deprecation("Input '%s' has units='unitless' but 'unitless' "
                               "has been deprecated. Use "
                               "units=None instead.  Note that connecting a "
                               "unitless variable to one with units is no longer "
                               "an error, but will issue a warning instead." %
                               name)
              units = None
  
          # First, type check all arguments
          if not isinstance(name, str):
              raise TypeError('The name argument should be a string')
          if not _valid_var_name(name):
              raise NameError("'%s' is not a valid input name." % name)
          if not isscalar(val) and not isinstance(val, (list, tuple, ndarray, Iterable)):
              raise TypeError('The val argument should be a float, list, tuple, ndarray or Iterable')
          if shape is not None and not isinstance(shape, (int, tuple, list, np.integer)):
              raise TypeError("The shape argument should be an int, tuple, or list but "
                              "a '%s' was given" % type(shape))
          if src_indices is not None and not isinstance(src_indices, (int, list, tuple,
                                                                      ndarray, Iterable)):
              raise TypeError('The src_indices argument should be an int, list, '
                              'tuple, ndarray or Iterable')
          if units is not None and not isinstance(units, str):
              raise TypeError('The units argument should be a str or None')
  
          # Check that units are valid
          if units is not None and not valid_units(units):
              raise ValueError("The units '%s' are invalid" % units)
  
          metadata = {}
  
          # value, shape: based on args, making sure they are compatible
          metadata['value'], metadata['shape'], src_indices = ensure_compatible(name, val, shape,
                                                                                src_indices)
          metadata['size'] = np.prod(metadata['shape'])
  
          # src_indices: None or ndarray
          if src_indices is None:
              metadata['src_indices'] = None
          else:
              metadata['src_indices'] = np.asarray(src_indices, dtype=INT_DTYPE)
          metadata['flat_src_indices'] = flat_src_indices
  
          metadata['units'] = units
          metadata['desc'] = desc
          metadata['distributed'] = self.options['distributed']
  
          # We may not know the pathname yet, so we have to use name for now, instead of abs_name.
          if self._static_mode:
              var_rel2meta = self._static_var_rel2meta
              var_rel_names = self._static_var_rel_names
          else:
              var_rel2meta = self._var_rel2meta
              var_rel_names = self._var_rel_names
  
          # Disallow dupes
          if name in var_rel2meta:
              msg = "Variable name '{}' already exists.".format(name)
              raise ValueError(msg)
  
          var_rel2meta[name] = metadata
          var_rel_names['input'].append(name)
  
          return metadata
  
      def add_discrete_input(self, name, val, desc=''):
          """
          Add a discrete input variable to the component.
  
          Parameters
          ----------
          name : str
              name of the variable in this component's namespace.
          val : a picklable object
              The initial value of the variable being added.
          desc : str
              description of the variable
  
          Returns
          -------
          dict
              metadata for added variable
          """
          # First, type check all arguments
          if not isinstance(name, str):
              raise TypeError('The name argument should be a string')
          if not _valid_var_name(name):
              raise NameError("'%s' is not a valid input name." % name)
  
          metadata = {
              'value': val,
              'type': type(val),
              'desc': desc,
          }
  
          if self._static_mode:
              var_rel2meta = self._static_var_rel2meta
          else:
              var_rel2meta = self._var_rel2meta
  
          # Disallow dupes
          if name in var_rel2meta:
              msg = "Variable name '{}' already exists.".format(name)
              raise ValueError(msg)
  
          var_rel2meta[name] = self._var_discrete['input'][name] = metadata
  
          return metadata
  
      def add_output(self, name, val=1.0, shape=None, units=None, res_units=None, desc='',
                     lower=None, upper=None, ref=1.0, ref0=0.0, res_ref=1.0):
          """
          Add an output variable to the component.
  
          Parameters
          ----------
          name : str
              name of the variable in this component's namespace.
          val : float or list or tuple or ndarray
              The initial value of the variable being added in user-defined units. Default is 1.0.
          shape : int or tuple or list or None
              Shape of this variable, only required if val is not an array.
              Default is None.
          units : str or None
              Units in which the output variables will be provided to the component during execution.
              Default is None, which means it has no units.
          res_units : str or None
              Units in which the residuals of this output will be given to the user when requested.
              Default is None, which means it has no units.
          desc : str
              description of the variable.
          lower : float or list or tuple or ndarray or Iterable or None
              lower bound(s) in user-defined units. It can be (1) a float, (2) an array_like
              consistent with the shape arg (if given), or (3) an array_like matching the shape of
              val, if val is array_like. A value of None means this output has no lower bound.
              Default is None.
          upper : float or list or tuple or ndarray or or Iterable None
              upper bound(s) in user-defined units. It can be (1) a float, (2) an array_like
              consistent with the shape arg (if given), or (3) an array_like matching the shape of
              val, if val is array_like. A value of None means this output has no upper bound.
              Default is None.
          ref : float or ndarray
              Scaling parameter. The value in the user-defined units of this output variable when
              the scaled value is 1. Default is 1.
          ref0 : float or ndarray
              Scaling parameter. The value in the user-defined units of this output variable when
              the scaled value is 0. Default is 0.
          res_ref : float or ndarray
              Scaling parameter. The value in the user-defined res_units of this output's residual
              when the scaled value is 1. Default is 1.
  
          Returns
          -------
          dict
              metadata for added variable
          """
          if units == 'unitless':
              warn_deprecation("Output '%s' has units='unitless' but 'unitless' "
                               "has been deprecated. Use "
                               "units=None instead.  Note that connecting a "
                               "unitless variable to one with units is no longer "
                               "an error, but will issue a warning instead." %
                               name)
              units = None
  
          if not isinstance(name, str):
              raise TypeError('The name argument should be a string')
          if not _valid_var_name(name):
              raise NameError("'%s' is not a valid output name." % name)
          if not isscalar(val) and not isinstance(val, (list, tuple, ndarray, Iterable)):
              msg = 'The val argument should be a float, list, tuple, ndarray or Iterable'
              raise TypeError(msg)
          if not isscalar(ref) and not isinstance(val, (list, tuple, ndarray, Iterable)):
              msg = 'The ref argument should be a float, list, tuple, ndarray or Iterable'
              raise TypeError(msg)
          if not isscalar(ref0) and not isinstance(val, (list, tuple, ndarray, Iterable)):
              msg = 'The ref0 argument should be a float, list, tuple, ndarray or Iterable'
              raise TypeError(msg)
          if not isscalar(res_ref) and not isinstance(val, (list, tuple, ndarray, Iterable)):
              msg = 'The res_ref argument should be a float, list, tuple, ndarray or Iterable'
              raise TypeError(msg)
          if shape is not None and not isinstance(shape, (int, tuple, list, np.integer)):
              raise TypeError("The shape argument should be an int, tuple, or list but "
                              "a '%s' was given" % type(shape))
          if units is not None and not isinstance(units, str):
              raise TypeError('The units argument should be a str or None')
          if res_units is not None and not isinstance(res_units, str):
              raise TypeError('The res_units argument should be a str or None')
  
          # Check that units are valid
          if units is not None and not valid_units(units):
              raise ValueError("The units '%s' are invalid" % units)
  
          metadata = {}
  
          # value, shape: based on args, making sure they are compatible
          metadata['value'], metadata['shape'], _ = ensure_compatible(name, val, shape)
          metadata['size'] = np.prod(metadata['shape'])
  
          # units, res_units: taken as is
          metadata['units'] = units
          metadata['res_units'] = res_units
  
          # desc: taken as is
          metadata['desc'] = desc
  
          if lower is not None:
              lower = ensure_compatible(name, lower, metadata['shape'])[0]
          if upper is not None:
              upper = ensure_compatible(name, upper, metadata['shape'])[0]
  
          metadata['lower'] = lower
          metadata['upper'] = upper
  
          # All refs: check the shape if necessary
          for item, item_name in zip([ref, ref0, res_ref], ['ref', 'ref0', 'res_ref']):
              if not isscalar(item):
                  it = atleast_1d(item)
                  if it.shape != metadata['shape']:
                      raise ValueError("'{}': When adding output '{}', expected shape {} but got "
                                       "shape {} for argument '{}'.".format(self.name, name,
                                                                            metadata['shape'],
                                                                            it.shape, item_name))
  
          if isscalar(ref):
              self._has_output_scaling |= ref != 1.0
          else:
              self._has_output_scaling |= np.any(ref != 1.0)
  
          if isscalar(ref0):
              self._has_output_scaling |= ref0 != 0.0
          else:
              self._has_output_scaling |= np.any(ref0)
  
          if isscalar(res_ref):
              self._has_resid_scaling |= res_ref != 1.0
          else:
              self._has_resid_scaling |= np.any(res_ref != 1.0)
  
          ref = format_as_float_or_array('ref', ref, flatten=True)
          ref0 = format_as_float_or_array('ref0', ref0, flatten=True)
          res_ref = format_as_float_or_array('res_ref', res_ref, flatten=True)
  
          metadata['ref'] = ref
          metadata['ref0'] = ref0
          metadata['res_ref'] = res_ref
  
          metadata['distributed'] = self.options['distributed']
  
          # We may not know the pathname yet, so we have to use name for now, instead of abs_name.
          if self._static_mode:
              var_rel2meta = self._static_var_rel2meta
              var_rel_names = self._static_var_rel_names
          else:
              var_rel2meta = self._var_rel2meta
              var_rel_names = self._var_rel_names
  
          # Disallow dupes
          if name in var_rel2meta:
              msg = "Variable name '{}' already exists.".format(name)
              raise ValueError(msg)
  
          var_rel2meta[name] = metadata
          var_rel_names['output'].append(name)
  
          return metadata
  
      def add_discrete_output(self, name, val, desc=''):
          """
          Add an output variable to the component.
  
          Parameters
          ----------
          name : str
              name of the variable in this component's namespace.
          val : a picklable object
              The initial value of the variable being added.
          desc : str
              description of the variable.
  
          Returns
          -------
          dict
              metadata for added variable
          """
          if not isinstance(name, str):
              raise TypeError('The name argument should be a string')
          if not _valid_var_name(name):
              raise NameError("'%s' is not a valid output name." % name)
  
          metadata = {
              'value': val,
              'type': type(val),
              'desc': desc
          }
  
          if self._static_mode:
              var_rel2meta = self._static_var_rel2meta
          else:
              var_rel2meta = self._var_rel2meta
  
          # Disallow dupes
          if name in var_rel2meta:
              msg = "Variable name '{}' already exists.".format(name)
              raise ValueError(msg)
  
          var_rel2meta[name] = self._var_discrete['output'][name] = metadata
  
          return metadata
  
      def _approx_partials(self, of, wrt, method='fd', **kwargs):
          """
          Inform the framework that the specified derivatives are to be approximated.
  
          Parameters
          ----------
          of : str or list of str
              The name of the residual(s) that derivatives are being computed for.
              May also contain a glob pattern.
          wrt : str or list of str
              The name of the variables that derivatives are taken with respect to.
              This can contain the name of any input or output variable.
              May also contain a glob pattern.
          method : str
              The type of approximation that should be used. Valid options include:
                  - 'fd': Finite Difference
          **kwargs : dict
              Keyword arguments for controlling the behavior of the approximation.
          """
          pattern_matches = self._find_partial_matches(of, wrt)
  
          for of_bundle, wrt_bundle in product(*pattern_matches):
              of_pattern, of_matches = of_bundle
              wrt_pattern, wrt_matches = wrt_bundle
              if not of_matches:
                  raise ValueError('No matches were found for of="{}"'.format(of_pattern))
              if not wrt_matches:
                  raise ValueError('No matches were found for wrt="{}"'.format(wrt_pattern))
  
              info = self._subjacs_info
              for rel_key in product(of_matches, wrt_matches):
                  abs_key = rel_key2abs_key(self, rel_key)
                  if abs_key in info:
                      meta = info[abs_key]
                  else:
                      meta = SUBJAC_META_DEFAULTS.copy()
                  meta['method'] = method
                  meta.update(kwargs)
                  info[abs_key] = meta
  
      def declare_partials(self, of, wrt, dependent=True, rows=None, cols=None, val=None,
                           method='exact', step=None, form=None, step_calc=None):
          """
          Declare information about this component's subjacobians.
  
          Parameters
          ----------
          of : str or list of str
              The name of the residual(s) that derivatives are being computed for.
              May also contain a glob pattern.
          wrt : str or list of str
              The name of the variables that derivatives are taken with respect to.
              This can contain the name of any input or output variable.
              May also contain a glob pattern.
          dependent : bool(True)
              If False, specifies no dependence between the output(s) and the
              input(s). This is only necessary in the case of a sparse global
              jacobian, because if 'dependent=False' is not specified and
              declare_partials is not called for a given pair, then a dense
              matrix of zeros will be allocated in the sparse global jacobian
              for that pair.  In the case of a dense global jacobian it doesn't
              matter because the space for a dense subjac will always be
              allocated for every pair.
          rows : ndarray of int or None
              Row indices for each nonzero entry.  For sparse subjacobians only.
          cols : ndarray of int or None
              Column indices for each nonzero entry.  For sparse subjacobians only.
          val : float or ndarray of float or scipy.sparse
              Value of subjacobian.  If rows and cols are not None, this will
              contain the values found at each (row, col) location in the subjac.
          method : str
              The type of approximation that should be used. Valid options include:
              'fd': Finite Difference, 'cs': Complex Step, 'exact': use the component
              defined analytic derivatives. Default is 'exact'.
          step : float
              Step size for approximation. Defaults to None, in which case the approximation
              method provides its default value.
          form : string
              Form for finite difference, can be 'forward', 'backward', or 'central'. Defaults
              to None, in which case the approximation method provides its default value.
          step_calc : string
              Step type for finite difference, can be 'abs' for absolute', or 'rel' for
              relative. Defaults to None, in which case the approximation method provides
              its default value.
          """
          try:
              method_func, default_opts = _supported_methods[method]
          except KeyError:
              msg = 'Method "{}" is not supported, method must be one of {}'
              raise ValueError(msg.format(method, _supported_methods.keys()))
  
          # Analytic Derivative for this Jacobian pair
          if method_func is None:  # exact
  
              # If only one of rows/cols is specified
              if (rows is None) ^ (cols is None):
                  raise ValueError('If one of rows/cols is specified, then both must be specified')
  
              if rows is not None:
                  # check for repeated rows/cols indices
                  idxset = set(zip(rows, cols))
                  if len(rows) - len(idxset) > 0:
                      dups = [n for n, val in iteritems(Counter(zip(rows, cols))) if val > 1]
                      raise RuntimeError("%s: declare_partials has been called with rows and cols "
                                         "that specify the following duplicate subjacobian entries: "
                                         "%s." % (self.pathname, sorted(dups)))
  
              self._declared_partials.append((of, wrt, dependent, rows, cols, val))
  
          # Approximation of the derivative, former API call approx_partials.
          else:
  
              if method not in self._approx_schemes:
                  self._approx_schemes[method] = method_func()
  
              # If rows/cols is specified
              if rows is not None or cols is not None:
                  raise ValueError('Sparse FD specification not supported yet.')
  
              # Need to declare the Jacobian element too.
              self._declared_partials.append((of, wrt, True, rows, cols, val))
  
              kwargs = {}
              if step:
                  if 'step' in default_opts:
                      kwargs['step'] = step
                  else:
                      raise RuntimeError("'step' is not a valid option for '%s'" % method)
              if form:
                  if 'form' in default_opts:
                      kwargs['form'] = form
                  else:
                      raise RuntimeError("'form' is not a valid option for '%s'" % method)
              if step_calc:
                  if 'step_calc' in default_opts:
                      kwargs['step_calc'] = step_calc
                  else:
                      raise RuntimeError("'step_calc' is not a valid option for '%s'" % method)
  
              self._approximated_partials.append((of, wrt, method, kwargs))
  
      def set_check_partial_options(self, wrt, method='fd', form=None, step=None, step_calc=None,
                                    directional=False):
          """
          Set options that will be used for checking partial derivatives.
  
          Parameters
          ----------
          wrt : str or list of str
              The name or names of the variables that derivatives are taken with respect to.
              This can contain the name of any input or output variable.
              May also contain a glob pattern.
          method : str
              Method for check: "fd" for finite difference, "cs" for complex step.
          form : str
              Finite difference form for check, can be "forward", "central", or "backward". Leave
              undeclared to keep unchanged from previous or default value.
          step : float
              Step size for finite difference check. Leave undeclared to keep unchanged from previous
              or default value.
          step_calc : str
              Type of step calculation for check, can be "abs" for absolute (default) or "rel" for
              relative.  Leave undeclared to keep unchanged from previous or default value.
          directional : bool
              Set to True to perform a single directional derivative for each vector variable in the
              pattern named in wrt.
          """
          supported_methods = ('fd', 'cs')
          if method not in supported_methods:
              msg = "Method '{}' is not supported, method must be one of {}"
              raise ValueError(msg.format(method, supported_methods))
  
          if step and not isinstance(step, (int, float)):
              msg = "The value of 'step' must be numeric, but '{}' was specified."
              raise ValueError(msg.format(step))
  
          supported_step_calc = ('abs', 'rel')
          if step_calc and step_calc not in supported_step_calc:
              msg = "The value of 'step_calc' must be one of {}, but '{}' was specified."
              raise ValueError(msg.format(supported_step_calc, step_calc))
  
          if not isinstance(wrt, (string_types, list, tuple)):
              msg = "The value of 'wrt' must be a string or list of strings, but a type " \
                    "of '{}' was provided."
              raise ValueError(msg.format(type(wrt).__name__))
  
          if not isinstance(directional, bool):
              msg = "The value of 'directional' must be True or False, but a type " \
                    "of '{}' was provided."
              raise ValueError(msg.format(type(directional).__name__))
  
          wrt_list = [wrt] if isinstance(wrt, string_types) else wrt
          self._declared_partial_checks.append((wrt_list, method, form, step, step_calc,
                                                directional))
  
      def _get_check_partial_options(self):
          """
          Return dictionary of partial options with pattern matches processed.
  
          This is called by check_partials.
  
          Returns
          -------
          dict(wrt : (options))
              Dictionary keyed by name with tuples of options (method, form, step, step_calc)
          """
          opts = {}
          outs = list(self._var_allprocs_prom2abs_list['output'].keys())
          ins = list(self._var_allprocs_prom2abs_list['input'].keys())
  
          invalid_wrt = []
  
          for wrt_list, method, form, step, step_calc, directional in self._declared_partial_checks:
              for pattern in wrt_list:
                  matches = find_matches(pattern, outs + ins)
  
                  # if a non-wildcard var name was specified and not found, save for later Exception
                  if len(matches) == 0 and _valid_var_name(pattern):
                      invalid_wrt.append(pattern)
  
                  for match in matches:
                      if match in opts:
                          opt = opts[match]
  
                          # New assignments take precedence
                          keynames = ['method', 'form', 'step', 'step_calc', 'directional']
                          for name, value in zip(keynames,
                                                 [method, form, step, step_calc, directional]):
                              if value is not None:
                                  opt[name] = value
  
                      else:
                          opts[match] = {'method': method,
                                         'form': form,
                                         'step': step,
                                         'step_calc': step_calc,
                                         'directional': directional}
  
          if invalid_wrt:
              if len(invalid_wrt) == 1:
                  msg = "Invalid 'wrt' variable specified for check_partial options on Component " \
                        "'{}': '{}'.".format(self.pathname, invalid_wrt[0])
              else:
                  msg = "Invalid 'wrt' variables specified for check_partial options on Component " \
                        "'{}': {}.".format(self.pathname, invalid_wrt)
              raise ValueError(msg)
  
          return opts
  
      def _declare_partials(self, of, wrt, dependent=True, rows=None, cols=None, val=None):
          """
          Store subjacobian metadata for later use.
  
          Parameters
          ----------
          of : str or list of str
              The name of the residual(s) that derivatives are being computed for.
              May also contain a glob pattern.
          wrt : str or list of str
              The name of the variables that derivatives are taken with respect to.
              This can contain the name of any input or output variable.
              May also contain a glob pattern.
          dependent : bool(True)
              If False, specifies no dependence between the output(s) and the
              input(s). This is only necessary in the case of a sparse global
              jacobian, because if 'dependent=False' is not specified and
              declare_partials is not called for a given pair, then a dense
              matrix of zeros will be allocated in the sparse global jacobian
              for that pair.  In the case of a dense global jacobian it doesn't
              matter because the space for a dense subjac will always be
              allocated for every pair.
          rows : ndarray of int or None
              Row indices for each nonzero entry.  For sparse subjacobians only.
          cols : ndarray of int or None
              Column indices for each nonzero entry.  For sparse subjacobians only.
          val : float or ndarray of float or scipy.sparse
              Value of subjacobian.  If rows and cols are not None, this will
              contain the values found at each (row, col) location in the subjac.
          """
          is_scalar = isscalar(val)
  
          if dependent:
              if rows is None:
                  if val is not None and not is_scalar and not issparse(val):
                      val = atleast_2d(val)
                      val = val.astype(promote_types(val.dtype, float), copy=False)
                  rows_max = cols_max = 0
              else:  # sparse list format
                  rows = np.array(rows, dtype=INT_DTYPE, copy=False)
                  cols = np.array(cols, dtype=INT_DTYPE, copy=False)
  
                  if rows.shape != cols.shape:
                      raise ValueError('rows and cols must have the same shape,'
                                       ' rows: {}, cols: {}'.format(rows.shape, cols.shape))
  
                  if is_scalar:
                      val = np.full(rows.size, val, dtype=float)
                      is_scalar = False
                  elif val is not None:
                      # np.promote_types will choose the smallest dtype that can contain
                      # both arguments
                      val = atleast_1d(val)
                      safe_dtype = promote_types(val.dtype, float)
                      val = val.astype(safe_dtype, copy=False)
  
                      if rows.shape != val.shape:
                          raise ValueError('If rows and cols are specified, val must be a scalar or '
                                           'have the same shape, val: {}, '
                                           'rows/cols: {}'.format(val.shape, rows.shape))
                  else:
                      val = np.zeros_like(rows, dtype=float)
  
                  if rows.size > 0:
                      if rows.min() < 0:
                          msg = '{}: d({})/d({}): row indices must be non-negative'
                          raise ValueError(msg.format(self.pathname, of, wrt))
                      if cols.min() < 0:
                          msg = '{}: d({})/d({}): col indices must be non-negative'
                          raise ValueError(msg.format(self.pathname, of, wrt))
                      rows_max = rows.max()
                      cols_max = cols.max()
                  else:
                      rows_max = cols_max = 0
  
          pattern_matches = self._find_partial_matches(of, wrt)
          abs2meta = self._var_abs2meta
  
          is_array = isinstance(val, ndarray)
  
          for of_bundle, wrt_bundle in product(*pattern_matches):
              of_pattern, of_matches = of_bundle
              wrt_pattern, wrt_matches = wrt_bundle
              if not of_matches:
                  raise ValueError('No matches were found for of="{}"'.format(of_pattern))
              if not wrt_matches:
                  raise ValueError('No matches were found for wrt="{}"'.format(wrt_pattern))
  
              for rel_key in product(of_matches, wrt_matches):
                  abs_key = rel_key2abs_key(self, rel_key)
                  if not dependent:
                      if abs_key in self._subjacs_info:
                          del self._subjacs_info[abs_key]
                      continue
  
                  if abs_key in self._subjacs_info:
                      meta = self._subjacs_info[abs_key]
                  else:
                      meta = SUBJAC_META_DEFAULTS.copy()
  
                  meta['rows'] = rows
                  meta['cols'] = cols
                  meta['dependent'] = dependent
                  meta['shape'] = shape = (abs2meta[abs_key[0]]['size'], abs2meta[abs_key[1]]['size'])
  
                  if val is None:
                      # we can only get here if rows is None  (we're not sparse list format)
                      meta['value'] = np.zeros(shape)
                  elif is_array:
                      if rows is None and val.shape != shape and val.size == shape[0] * shape[1]:
                          meta['value'] = val = val.copy().reshape(shape)
                      else:
                          meta['value'] = val.copy()
                  elif is_scalar:
                      meta['value'] = np.full(shape, val, dtype=float)
                  else:
                      meta['value'] = val
  
                  if rows_max >= shape[0] or cols_max >= shape[1]:
                      of, wrt = abs_key2rel_key(self, abs_key)
                      msg = '{}: d({})/d({}): Expected {}x{} but declared at least {}x{}'
                      raise ValueError(msg.format(self.pathname, of, wrt, shape[0], shape[1],
                                                  rows_max + 1, cols_max + 1))
  
                  self._check_partials_meta(abs_key, meta['value'],
                                            shape if rows is None else (rows.shape[0], 1))
                  self._subjacs_info[abs_key] = meta
  
      def _find_partial_matches(self, of, wrt):
          """
          Find all partial derivative matches from of and wrt.
  
          Parameters
          ----------
          of : str or list of str
              The relative name of the residual(s) that derivatives are being computed for.
              May also contain a glob pattern.
          wrt : str or list of str
              The relative name of the variables that derivatives are taken with respect to.
              This can contain the name of any input or output variable.
              May also contain a glob pattern.
  
          Returns
          -------
          tuple(list, list)
              Pair of lists containing pattern matches (if any). Returns (of_matches, wrt_matches)
              where of_matches is a list of tuples (pattern, matches) and wrt_matches is a list of
              tuples (pattern, output_matches, input_matches).
          """
          of_list = [of] if isinstance(of, string_types) else of
          wrt_list = [wrt] if isinstance(wrt, string_types) else wrt
          outs = list(self._var_allprocs_prom2abs_list['output'])
          ins = list(self._var_allprocs_prom2abs_list['input'])
  
          of_pattern_matches = [(pattern, find_matches(pattern, outs)) for pattern in of_list]
          wrt_pattern_matches = [(pattern, find_matches(pattern, outs + ins)) for pattern in wrt_list]
          return of_pattern_matches, wrt_pattern_matches
  
      def _check_partials_meta(self, abs_key, val, shape):
          """
          Check a given partial derivative and metadata for the correct shapes.
  
          Parameters
          ----------
          abs_key : tuple(str, str)
              The of/wrt pair (given absolute names) defining the partial derivative.
          val : ndarray
              Subjac value.
          shape : tuple
              Expected shape of val.
          """
          out_size, in_size = shape
  
          if in_size == 0 and self.comm.rank != 0:  # 'inactive' component
              return
  
          if val is not None:
              val_shape = val.shape
              if len(val_shape) == 1:
                  val_out, val_in = val_shape[0], 1
              else:
                  val_out, val_in = val.shape
              if val_out > out_size or val_in > in_size:
                  of, wrt = abs_key2rel_key(self, abs_key)
                  msg = '{}: d({})/d({}): Expected {}x{} but val is {}x{}'
                  raise ValueError(msg.format(self.pathname, of, wrt, out_size, in_size,
                                              val_out, val_in))
  
      def _set_partials_meta(self):
          """
          Set subjacobian info into our jacobian.
          """
          for key, meta in iteritems(self._subjacs_info):
  
              if 'method' in meta:
                  method = meta['method']
                  if method is not None and method in self._approx_schemes:
                      self._approx_schemes[method].add_approximation(key, meta)
  
      def _guess_nonlinear(self):
          """
          Provide initial guess for states.
  
          Does nothing on any non-implicit component.
          """
          pass
  
      def _clear_iprint(self):
          """
          Clear out the iprint stack from the solvers.
  
          Components don't have nested solvers, so do nothing to prevent errors.
          """
          pass
  
  
  class _DictValues(object):
      """
      A dict-like wrapper for a dict of metadata, where getitem returns 'value' from metadata.
      """
  
      def __init__(self, dct):
          self._dict = dct
  
      def __getitem__(self, key):
          return self._dict[key]['value']
  
      def __setitem__(self, key, value):
          self._dict[key]['value'] = value
  
      def __contains__(self, key):
          return key in self._dict
  
      def __len__(self):
          return len(self._dict)
  