def __init__(self, system, inputs, outputs):
""" Performs finite difference on the components in a given
pseudo_assembly. """
self.inputs = inputs
self.outputs = outputs
self.in_bounds = {}
self.system = system
self.scope = system.scope
in_size = 0
for srcs in self.inputs:
# Support for parameter groups
if isinstance(srcs, basestring):
srcs = [srcs]
val = self.scope.get(srcs[0])
width = flattened_size(srcs[0], val, self.scope)
for src in srcs:
self.in_bounds[src] = (in_size, in_size+width)
in_size += width
out_size = 0
for src in self.outputs:
val = self.scope.get(src)
width = flattened_size(src, val)
out_size += width
self.y_base = zeros((out_size,))
self.y = zeros((out_size,))
self.y2 = zeros((out_size,))
def provideJ(self):
"""Calculate analytical first derivatives."""
if self.Jsize is None:
n_in = 0
n_out = 0
for varname in self.list_inputs():
val = self.get(varname)
width = flattened_size(varname, val, self)
n_in += width
for varname in self.list_outputs():
val = self.get(varname)
width = flattened_size(varname, val, self)
n_out += width
self.Jsize = (n_out, n_in)
J = zeros(self.Jsize)
grad = self._srcexpr.evaluate_gradient()
i = 0
for varname in self._inputs:
val = self.get(varname)
width = flattened_size(varname, val, self)
J[:, i:i+width] = grad[varname]
i += width
return J
def provideJ(self):
"""Calculate analytical first derivatives."""
if self.Jsize is None:
n_in = 0
n_out = 0
for varname in self.list_inputs():
val = self.get(varname)
width = flattened_size(varname, val, self)
n_in += width
for varname in self.list_outputs():
val = self.get(varname)
width = flattened_size(varname, val, self)
n_out += width
self.Jsize = (n_out, n_in)
J = zeros(self.Jsize)
grad = self._srcexpr.evaluate_gradient()
i = 0
for varname in self._inputs:
val = self.get(varname)
width = flattened_size(varname, val, self)
J[:, i:i + width] = grad[varname]
i += width
return J
def __init__(self, pa):
""" Performs finite difference on the components in a given
pseudo_assembly. """
self.inputs = pa.inputs
self.outputs = pa.outputs
self.in_bounds = {}
self.out_bounds = {}
self.pa = pa
self.scope = pa.wflow.scope
in_size = 0
for srcs in self.inputs:
# Support for parameter groups
if isinstance(srcs, basestring):
srcs = [srcs]
val = self.scope.get(srcs[0])
width = flattened_size(srcs[0], val, self.scope)
for src in srcs:
self.in_bounds[src] = (in_size, in_size+width)
in_size += width
out_size = 0
for src in self.outputs:
val = self.scope.get(src)
width = flattened_size(src, val)
self.out_bounds[src] = (out_size, out_size+width)
out_size += width
self.y_base = zeros((out_size,))
self.y = zeros((out_size,))
self.y2 = zeros((out_size,))
def get_bounds(obj, input_keys, output_keys, J):
""" Returns a pair of dictionaries that contain the stop and end index
for each input and output in a pair of lists.
"""
ibounds = {}
nvar = 0
scope = getattr(obj, 'parent', None)
for key in input_keys:
# For parameter group, all should be equal so just get first.
if not isinstance(key, tuple):
key = [key]
val = obj.get(key[0])
width = flattened_size('.'.join((obj.name, key[0])), val,
scope=scope)
shape = getattr(val, 'shape', None)
for item in key:
ibounds[item] = (nvar, nvar+width, shape)
nvar += width
num_input = nvar
obounds = {}
nvar = 0
for key in output_keys:
val = obj.get(key)
width = flattened_size('.'.join((obj.name, key)), val)
shape = getattr(val, 'shape', None)
obounds[key] = (nvar, nvar+width, shape)
nvar += width
num_output = nvar
if num_input and num_output:
# Give the user an intelligible error if the size of J is wrong.
try:
J_output, J_input = J.shape
except ValueError as err:
exc_type, value, traceback = sys.exc_info()
msg = "Jacobian has the wrong dimensions. Expected 2D but got {}D."
msg = msg.format(J.ndim)
raise ValueError, ValueError(msg), traceback
if num_output != J_output or num_input != J_input:
msg = 'Jacobian is the wrong size. Expected ' + \
'(%dx%d) but got (%dx%d)' % (num_output, num_input,
J_output, J_input)
if ISystem.providedBy(obj):
raise RuntimeError(msg)
else:
obj.raise_exception(msg, RuntimeError)
return ibounds, obounds
def get_bounds(obj, input_keys, output_keys, J):
""" Returns a pair of dictionaries that contain the stop and end index
for each input and output in a pair of lists.
"""
ibounds = {}
nvar = 0
scope = getattr(obj, 'parent', None)
for key in input_keys:
# For parameter group, all should be equal so just get first.
if not isinstance(key, tuple):
key = [key]
val = obj.get(key[0])
width = flattened_size('.'.join((obj.name, key[0])), val, scope=scope)
shape = getattr(val, 'shape', None)
for item in key:
ibounds[item] = (nvar, nvar + width, shape)
nvar += width
num_input = nvar
obounds = {}
nvar = 0
for key in output_keys:
val = obj.get(key)
width = flattened_size('.'.join((obj.name, key)), val)
shape = getattr(val, 'shape', None)
obounds[key] = (nvar, nvar + width, shape)
nvar += width
num_output = nvar
if num_input and num_output:
# Give the user an intelligible error if the size of J is wrong.
try:
J_output, J_input = J.shape
except ValueError as err:
exc_type, value, traceback = sys.exc_info()
msg = "Jacobian has the wrong dimensions. Expected 2D but got {}D."
msg = msg.format(J.ndim)
raise ValueError, ValueError(msg), traceback
if num_output != J_output or num_input != J_input:
msg = 'Jacobian is the wrong size. Expected ' + \
'(%dx%d) but got (%dx%d)' % (num_output, num_input,
J_output, J_input)
if ISystem.providedBy(obj):
raise RuntimeError(msg)
else:
obj.raise_exception(msg, RuntimeError)
return ibounds, obounds
def get_bounds(obj, input_keys, output_keys, J):
""" Returns a pair of dictionaries that contain the stop and end index
for each input and output in a pair of lists.
"""
ibounds = {}
nvar = 0
if hasattr(obj, 'parent'):
scope = obj.parent
else:
scope = None # Pseudoassys
for key in input_keys:
# For parameter group, all should be equal so just get first.
if not isinstance(key, tuple):
key = [key]
val = obj.get(key[0])
width = flattened_size('.'.join((obj.name, key[0])), val, scope=scope)
shape = val.shape if hasattr(val, 'shape') else None
for item in key:
ibounds[item] = (nvar, nvar + width, shape)
nvar += width
num_input = nvar
obounds = {}
nvar = 0
for key in output_keys:
val = obj.get(key)
width = flattened_size('.'.join((obj.name, key)), val)
shape = val.shape if hasattr(val, 'shape') else None
obounds[key] = (nvar, nvar + width, shape)
nvar += width
num_output = nvar
# Give the user an intelligible error if the size of J is wrong.
J_output, J_input = J.shape
if num_output != J_output or num_input != J_input:
msg = 'Jacobian is the wrong size. Expected ' + \
'(%dx%d) but got (%dx%d)' % (num_output, num_input,
J_output, J_input)
obj.raise_exception(msg, RuntimeError)
return ibounds, obounds
def get_bounds(obj, input_keys, output_keys, J):
""" Returns a pair of dictionaries that contain the stop and end index
for each input and output in a pair of lists.
"""
ibounds = {}
nvar = 0
scope = getattr(obj, 'parent', None)
for key in input_keys:
# For parameter group, all should be equal so just get first.
if not isinstance(key, tuple):
key = [key]
val = obj.get(key[0])
width = flattened_size('.'.join((obj.name, key[0])), val,
scope=scope)
shape = getattr(val, 'shape', None)
for item in key:
ibounds[item] = (nvar, nvar+width, shape)
nvar += width
num_input = nvar
obounds = {}
nvar = 0
for key in output_keys:
val = obj.get(key)
width = flattened_size('.'.join((obj.name, key)), val)
shape = getattr(val, 'shape', None)
obounds[key] = (nvar, nvar+width, shape)
nvar += width
num_output = nvar
if num_input and num_output:
# Give the user an intelligible error if the size of J is wrong.
J_output, J_input = J.shape
if num_output != J_output or num_input != J_input:
msg = 'Jacobian is the wrong size. Expected ' + \
'(%dx%d) but got (%dx%d)' % (num_output, num_input,
J_output, J_input)
obj.raise_exception(msg, RuntimeError)
return ibounds, obounds
def get_width(self, attr):
"""Return the flattened width of the value of the given attribute."""
width = self._width_cache.get(attr, _missing)
if width is _missing:
param = from_PA_var(attr)
self._width_cache[attr] = width = flattened_size(
param, self.scope.get(param), self.scope)
return width
def get_width(self, attr):
"""Return the flattened width of the value of the given attribute."""
width = self._width_cache.get(attr, _missing)
if width is _missing:
param = from_PA_var(attr)
self._width_cache[attr] = width = flattened_size(param,
self.scope.get(param),
self.scope)
return width
def get_flattened_size(self):
"""Return the size of a flattened float array containing
all values in the vartree that are flattenable to float
arrays. Any values not flattenable to float arrays will
raise a NoFlatError.
"""
size = 0
for key in self.list_vars():
size += flattened_size(key, getattr(self, key), scope=self)
return size
def get_bounds(obj, input_keys, output_keys):
""" Returns a pair of dictionaries that contain the stop and end index
for each input and output in a pair of lists.
"""
ibounds = {}
nvar = 0
if hasattr(obj, 'parent'):
scope = obj.parent
else:
scope = None # Pseudoassys
for key in input_keys:
# For parameter group, all should be equal so just get first.
if not isinstance(key, tuple):
key = [key]
val = obj.get(key[0])
width = flattened_size('.'.join((obj.name, key[0])), val,
scope=scope)
shape = val.shape if hasattr(val, 'shape') else None
for item in key:
ibounds[item] = (nvar, nvar+width, shape)
nvar += width
obounds = {}
nvar = 0
for key in output_keys:
val = obj.get(key)
width = flattened_size('.'.join((obj.name, key)), val)
shape = val.shape if hasattr(val, 'shape') else None
obounds[key] = (nvar, nvar+width, shape)
nvar += width
return ibounds, obounds
def __init__(self, pa):
""" Performs finite difference on the components in a given
pseudo_assembly. """
self.inputs = pa.inputs
self.outputs = pa.outputs
self.in_bounds = {}
self.out_bounds = {}
self.pa = pa
self.scope = pa.wflow.scope
options = pa.wflow._parent.gradient_options
self.fd_step = options.fd_step*ones((len(self.inputs)))
self.form = options.fd_form
self.form_custom = {}
self.step_type = options.fd_step_type
self.step_type_custom = {}
self.relative_threshold = 1.0e-4
driver = self.pa.wflow._parent
driver_params = []
driver_targets = []
if hasattr(driver, 'get_parameters'):
driver_params = self.pa.wflow._parent.get_parameters()
driver_targets = driver.list_param_targets()
in_size = 0
for j, srcs in enumerate(self.inputs):
low = high = None
# Support for parameter groups
if isinstance(srcs, basestring):
srcs = [srcs]
# Local stepsize support
meta = self.scope.get_metadata(self.scope._depgraph.base_var(srcs[0]))
if 'fd_step' in meta:
self.fd_step[j] = meta['fd_step']
if 'low' in meta:
low = meta[ 'low' ]
if 'high' in meta:
high = meta[ 'high' ]
if srcs[0] in driver_targets:
if srcs[0] in driver_params:
param = driver_params[srcs[0]]
if param.fd_step is not None:
self.fd_step[j] = param.fd_step
if param.low is not None:
low = param.low
if param.high is not None:
high = param.high
else:
# have to check through all the param groups
for param_group in driver_params:
is_fd_step_not_set = is_low_not_set = is_high_not_set = True
if not isinstance(param_group, str) and \
srcs[0] in param_group:
param = driver_params[param_group]
if is_fd_step_not_set and param.fd_step is not None:
self.fd_step[j] = param.fd_step
is_fd_step_not_set = False
if is_low_not_set and param.low is not None:
low = param.low
is_low_not_set = False
if is_high_not_set and param.high is not None:
high = param.high
is_high_not_set = False
if 'fd_step_type' in meta:
self.step_type_custom[j] = meta['fd_step_type']
step_type = self.step_type_custom[j]
else:
step_type = self.step_type
# Bounds scaled
if step_type == 'bounds_scaled':
if low is None and high is None :
raise RuntimeError("For variable '%s', a finite "
"difference step type of "
"bounds_scaled is used but required low and "
"high values are not set" % srcs[0] )
if low == - float_info.max:
raise RuntimeError("For variable '%s', a finite "
"difference step type of "
"bounds_scaled is used but required "
"low value is not set" % srcs[0] )
if high == float_info.max:
raise RuntimeError("For variable '%s', a finite "
"difference step type of "
"bounds_scaled is used but required "
"high value is not set" % srcs[0] )
self.fd_step[j] = ( high - low ) * self.fd_step[j]
if 'fd_form' in meta:
self.form_custom[j] = meta['fd_form']
val = self.scope.get(srcs[0])
width = flattened_size(srcs[0], val, self.scope)
for src in srcs:
self.in_bounds[src] = (in_size, in_size+width)
in_size += width
out_size = 0
for src in self.outputs:
val = self.scope.get(src)
width = flattened_size(src, val)
self.out_bounds[src] = (out_size, out_size+width)
out_size += width
self.J = zeros((out_size, in_size))
self.y_base = zeros((out_size,))
self.x = zeros((in_size,))
self.y = zeros((out_size,))
self.y2 = zeros((out_size,))
def calc_gradient(self,
inputs=None,
outputs=None,
upscope=False,
mode='auto'):
"""Returns the gradient of the passed outputs with respect to
all passed inputs.
inputs: list of strings or tuples of strings
List of input variables that we are taking derivatives with respect
to. They must be within this workflow's scope. If no inputs are
given, the parent driver's parameters are used. A tuple can be used
to link inputs together.
outputs: list of strings
List of output variables that we are taking derivatives of.
They must be within this workflow's scope. If no outputs are
given, the parent driver's objectives and constraints are used.
upscope: boolean
This is set to True when our workflow is part of a subassembly that
lies in a workflow that needs a gradient with respect to variables
outside of this workflow, so that the caches can be reset.
mode: string
Set to 'forward' for forward mode, 'adjoint' for adjoint mode,
'fd' for full-model finite difference (with fake finite
difference disabled), or 'auto' to let OpenMDAO determine the
correct mode.
"""
self._J_cache = {}
# User may request full-model finite difference.
if self._parent.gradient_options.force_fd == True:
mode = 'fd'
# This function can be called from a parent driver's workflow for
# assembly recursion. We have to clear our cache if that happens.
# We also have to clear it next time we arrive back in our workflow.
if upscope or self._upscoped:
self._derivative_graph = None
self._edges = None
self._comp_edges = None
self._upscoped = upscope
dgraph = self.derivative_graph(inputs, outputs, fd=(mode == 'fd'))
if 'mapped_inputs' in dgraph.graph:
inputs = dgraph.graph['mapped_inputs']
outputs = dgraph.graph['mapped_outputs']
else:
inputs = dgraph.graph['inputs']
outputs = dgraph.graph['outputs']
n_edge = self.initialize_residual()
# cache Jacobians for comps that return them from provideJ
# Size our Jacobian
num_in = 0
for item in inputs:
# For parameter groups, only size the first
if not isinstance(item, basestring):
item = item[0]
try:
i1, i2 = self.get_bounds(item)
if isinstance(i1, list):
num_in += len(i1)
else:
num_in += i2 - i1
except KeyError:
val = self.scope.get(item)
num_in += flattened_size(item, val, self.scope)
num_out = 0
for item in outputs:
try:
i1, i2 = self.get_bounds(item)
if isinstance(i1, list):
num_out += len(i1)
else:
num_out += i2 - i1
except KeyError:
val = self.scope.get(item)
num_out += flattened_size(item, val, self.scope)
shape = (num_out, num_in)
# Auto-determine which mode to use based on Jacobian shape.
if mode == 'auto':
# TODO - additional determination based on presence of
# apply_derivT
if num_in > num_out:
mode = 'adjoint'
else:
mode = 'forward'
if mode == 'adjoint':
J = calc_gradient_adjoint(self, inputs, outputs, n_edge, shape)
elif mode in ['forward', 'fd']:
J = calc_gradient(self, inputs, outputs, n_edge, shape)
else:
msg = "In calc_gradient, mode must be 'forward', 'adjoint', " + \
"'auto', or 'fd', but a value of %s was given." % mode
self.scope.raise_exception(msg, RuntimeError)
# Finally, we need to untransform the jacobian if any parameters have
# scalers.
#print 'edges:', self._edges
if not hasattr(self._parent, 'get_parameters'):
return J
params = self._parent.get_parameters()
if len(params) == 0:
return J
i = 0
for group in inputs:
if isinstance(group, str):
group = [group]
name = group[0]
if len(group) > 1:
pname = tuple([from_PA_var(aname) for aname in group])
else:
pname = from_PA_var(name)
try:
i1, i2 = self.get_bounds(name)
except KeyError:
continue
if isinstance(i1, list):
width = len(i1)
else:
width = i2 - i1
if pname in params:
scaler = params[pname].scaler
if scaler != 1.0:
J[:, i:i + width] = J[:, i:i + width] * scaler
i = i + width
#print J
return J
def initialize_residual(self):
"""Creates the array that stores the residual. Also returns the
number of edges.
"""
dgraph = self.derivative_graph()
if 'mapped_inputs' in dgraph.graph:
inputs = dgraph.graph['mapped_inputs']
else:
inputs = dgraph.graph['inputs']
basevars = set()
edges = self.edge_list()
implicit_edges = self.get_implicit_info()
sortedkeys = sorted(implicit_edges)
sortedkeys.extend(sorted(edges.keys()))
nEdge = 0
for src in sortedkeys:
if src in implicit_edges:
targets = implicit_edges[src]
is_implicit = True
else:
targets = edges[src]
is_implicit = False
if isinstance(targets, str):
targets = [targets]
# Implicit source edges are tuples.
if is_implicit == True:
impli_edge = nEdge
for resid in src:
unmap_src = from_PA_var(resid)
val = self.scope.get(unmap_src)
width = flattened_size(unmap_src, val, self.scope)
if isinstance(val, ndarray):
shape = val.shape
else:
shape = 1
bound = (impli_edge, impli_edge + width)
self.set_bounds(resid, bound)
basevars.add(resid)
impli_edge += width
# Regular components
else:
# Only need to grab the source (or first target for param) to
# figure out the size for the residual vector
measure_src = src
if '@in' in src:
idx = int(src[3:].split('[')[0])
inp = inputs[idx]
if not isinstance(inp, basestring):
inp = inp[0]
if inp in dgraph:
measure_src = inp
else:
measure_src = targets[0]
elif src == '@fake':
for t in targets:
if not t.startswith('@'):
measure_src = t
break
else:
raise RuntimeError("malformed graph!")
# Find our width, etc.
unmap_src = from_PA_var(measure_src)
val = self.scope.get(unmap_src)
width = flattened_size(unmap_src, val, self.scope)
if isinstance(val, ndarray):
shape = val.shape
else:
shape = 1
# Special poke for boundary node
if is_boundary_node(dgraph, measure_src) or \
is_boundary_node(dgraph, dgraph.base_var(measure_src)):
bound = (nEdge, nEdge + width)
self.set_bounds(measure_src, bound)
src_noidx = src.split('[', 1)[0]
# Poke our source data
# Array slice of src that is already allocated
if '[' in src and src_noidx in basevars:
_, _, idx = src.partition('[')
basebound = self.get_bounds(src_noidx)
if not '@in' in src_noidx:
unmap_src = from_PA_var(src_noidx)
val = self.scope.get(unmap_src)
shape = val.shape
offset = basebound[0]
istring, ix = flatten_slice(idx,
shape,
offset=offset,
name='ix')
bound = (istring, ix)
# Already allocated
width = 0
# Input-input connection to implicit state
elif src_noidx in basevars:
bound = self.get_bounds(src_noidx)
width = 0
# Normal src
else:
bound = (nEdge, nEdge + width)
self.set_bounds(src, bound)
basevars.add(src)
# Poke our target data
impli_edge = nEdge
for target in targets:
# Handle States in implicit comps
if is_implicit == True:
if isinstance(target, str):
target = [target]
unmap_targ = from_PA_var(target[0])
val = self.scope.get(unmap_targ)
imp_width = flattened_size(unmap_targ, val, self.scope)
if isinstance(val, ndarray):
shape = val.shape
else:
shape = 1
for itarget in target:
bound = (impli_edge, impli_edge + imp_width)
self.set_bounds(itarget, bound)
basevars.add(itarget)
impli_edge += imp_width
width = impli_edge - nEdge
elif not target.startswith('@'):
self.set_bounds(target, bound)
#print input_src, src, target, bound,
nEdge += width
impli_edge = nEdge
# Initialize the residual vector on the first time through, and also
# if for some reason the number of edges has changed.
if self.res is None or nEdge != self.res.shape[0]:
self.res = zeros((nEdge, 1))
return nEdge
def __init__(self, system, inputs, outputs, return_format='array'):
""" Performs finite difference on the components in a given
System. """
self.inputs = inputs
self.outputs = outputs
self.in_bounds = {}
self.system = system
self.scope = system.scope
self.return_format = return_format
options = system.options
driver = options.parent
self.fd_step = options.fd_step*ones((len(self.inputs)))
self.low = [None] * len(self.inputs)
self.high = [None] * len(self.inputs)
self.form = options.fd_form
self.form_custom = {}
self.step_type = options.fd_step_type
self.step_type_custom = {}
self.relative_threshold = 1.0e-4
dgraph = self.scope._depgraph
driver_params = []
driver_targets = []
if hasattr(driver, 'get_parameters'):
driver_params = driver.get_parameters()
driver_targets = driver.list_param_targets()
in_size = 0
for j, srcs in enumerate(self.inputs):
low = high = None
# Support for parameter groups
if isinstance(srcs, basestring):
srcs = [srcs]
# Local stepsize support
meta = self.scope.get_metadata(base_var(dgraph, srcs[0]))
if 'fd_step' in meta:
self.fd_step[j] = meta['fd_step']
if 'low' in meta:
low = meta['low']
if 'high' in meta:
high = meta['high']
# Settings in the add_parameter call trump all others
param_srcs = [item for item in srcs if item in driver_targets]
if param_srcs:
if param_srcs[0] in driver_params:
param = driver_params[param_srcs[0]]
if param.fd_step is not None:
self.fd_step[j] = param.fd_step
if param.low is not None:
low = param.low
if param.high is not None:
high = param.high
else:
# have to check through all the param groups
for param_group in driver_params:
is_fd_step_not_set = is_low_not_set = \
is_high_not_set = True
if not isinstance(param_group, str) and \
param_srcs[0] in param_group:
param = driver_params[param_group]
if is_fd_step_not_set and param.fd_step is not None:
self.fd_step[j] = param.fd_step
is_fd_step_not_set = False
if is_low_not_set and param.low is not None:
low = param.low
is_low_not_set = False
if is_high_not_set and param.high is not None:
high = param.high
is_high_not_set = False
if 'fd_step_type' in meta:
self.step_type_custom[j] = meta['fd_step_type']
step_type = self.step_type_custom[j]
else:
step_type = self.step_type
# Bounds scaled
if step_type == 'bounds_scaled':
if low is None and high is None:
raise RuntimeError("For variable '%s', a finite "
"difference step type of bounds_scaled "
"is used but required low and "
"high values are not set" % srcs[0])
if low == - float_info.max:
raise RuntimeError("For variable '%s', a finite "
"difference step type of "
"bounds_scaled is used but required "
"low value is not set" % srcs[0])
if high == float_info.max:
raise RuntimeError("For variable '%s', a finite "
"difference step type of "
"bounds_scaled is used but required "
"high value is not set" % srcs[0])
self.fd_step[j] = (high - low) * self.fd_step[j]
if 'fd_form' in meta:
self.form_custom[j] = meta['fd_form']
val = self.scope.get(srcs[0])
width = flattened_size(srcs[0], val, self.scope)
for src in srcs:
self.in_bounds[src] = (in_size, in_size+width)
in_size += width
self.high[j] = high
self.low[j] = low
out_size = 0
for src in self.outputs:
val = self.scope.get(src)
width = flattened_size(src, val)
out_size += width
# Size our Jacobian
if return_format == 'dict':
self.J = {}
for okey in outputs:
self.J[okey] = {}
for ikey in inputs:
if isinstance(ikey, tuple):
ikey = ikey[0]
# If output not on this process, just allocate a dummy
# array
if MPI and okey not in self.system.vec['u']:
osize = 0
else:
osize = self.system.vec['u'][okey].size
isize = self.system.vec['p'][ikey].size
self.J[okey][ikey] = zeros((osize, isize))
else:
self.J = zeros((out_size, in_size))
self.y_base = zeros((out_size,))
self.y = zeros((out_size,))
self.y2 = zeros((out_size,))
def calc_gradient(wflow, inputs, outputs, n_edge, shape):
"""Returns the gradient of the passed outputs with respect to
all passed inputs.
"""
# Size the problem
A = LinearOperator((n_edge, n_edge), matvec=wflow.matvecFWD, dtype=float)
J = zeros(shape)
# Each comp calculates its own derivatives at the current
# point. (i.e., linearizes)
wflow.calc_derivatives(first=True)
dgraph = wflow._derivative_graph
options = wflow._parent.gradient_options
# Forward mode, solve linear system for each parameter
j = 0
for param in inputs:
if isinstance(param, tuple):
# You can ask for derivatives of broadcast inputs in cases
# where some of the inputs aren't in the relevance graph.
# Find the one that is.
for bcast_param in param:
if bcast_param in dgraph and 'bounds' in dgraph.node[
bcast_param]:
param = bcast_param
break
else:
param = param[0]
#raise RuntimeError("didn't find any of '%s' in derivative graph for '%s'" %
#(param, wflow._parent.get_pathname()))
try:
i1, i2 = wflow.get_bounds(param)
except KeyError:
# If you end up here, it is usually because you have a
# tuple of broadcast inputs containing only non-relevant
# variables. Derivative is zero, so take one and increment
# by its width.
# TODO - We need to cache these when we remove
# boundcaching from the graph
val = wflow.scope.get(param)
j += flattened_size(param, val, wflow.scope)
continue
if isinstance(i1, list):
in_range = i1
else:
in_range = range(i1, i2)
for irhs in in_range:
RHS = zeros((n_edge, 1))
RHS[irhs, 0] = 1.0
# Call GMRES to solve the linear system
dx, info = gmres(A,
RHS,
tol=options.gmres_tolerance,
maxiter=options.gmres_maxiter)
if info > 0:
msg = "ERROR in calc_gradient in '%s': gmres failed to converge " \
"after %d iterations for parameter '%s' at index %d"
logger.error(msg %
(wflow._parent.get_pathname(), info, param, irhs))
elif info < 0:
msg = "ERROR in calc_gradient in '%s': gmres failed " \
"for parameter '%s' at index %d"
logger.error(msg % (wflow._parent.get_pathname(), param, irhs))
i = 0
for item in outputs:
try:
k1, k2 = wflow.get_bounds(item)
except KeyError:
continue
if isinstance(k1, list):
J[i:i + (len(k1)), j] = dx[k1]
i += len(k1)
else:
J[i:i + (k2 - k1), j] = dx[k1:k2]
i += k2 - k1
j += 1
#print inputs, '\n', outputs, '\n', J
return J
def __init__(self, system, inputs, outputs, return_format='array'):
""" Performs finite difference on the components in a given
System. """
self.inputs = inputs
self.outputs = outputs
self.in_bounds = {}
self.system = system
self.scope = system.scope
self.return_format = return_format
options = system.options
driver = options.parent
self.fd_step = options.fd_step*ones((len(self.inputs)))
self.low = [None] * len(self.inputs)
self.high = [None] * len(self.inputs)
self.form = options.fd_form
self.form_custom = {}
self.step_type = options.fd_step_type
self.step_type_custom = {}
self.relative_threshold = 1.0e-4
dgraph = self.scope._depgraph
driver_params = []
driver_targets = []
if hasattr(driver, 'get_parameters'):
driver_params = driver.get_parameters()
driver_targets = driver.list_param_targets()
in_size = 0
for j, srcs in enumerate(self.inputs):
low = high = None
# Support for parameter groups
if isinstance(srcs, basestring):
srcs = [srcs]
# Local stepsize support
meta = self.scope.get_metadata(base_var(dgraph, srcs[0]))
if 'fd_step' in meta:
self.fd_step[j] = meta['fd_step']
if 'low' in meta:
low = meta['low']
if 'high' in meta:
high = meta['high']
# Settings in the add_parameter call trump all others
param_srcs = [item for item in srcs if item in driver_targets]
if param_srcs:
if param_srcs[0] in driver_params:
param = driver_params[param_srcs[0]]
if param.fd_step is not None:
self.fd_step[j] = param.fd_step
if param.low is not None:
low = param.low
if param.high is not None:
high = param.high
else:
# have to check through all the param groups
for param_group in driver_params:
is_fd_step_not_set = is_low_not_set = \
is_high_not_set = True
if not isinstance(param_group, str) and \
param_srcs[0] in param_group:
param = driver_params[param_group]
if is_fd_step_not_set and param.fd_step is not None:
self.fd_step[j] = param.fd_step
is_fd_step_not_set = False
if is_low_not_set and param.low is not None:
low = param.low
is_low_not_set = False
if is_high_not_set and param.high is not None:
high = param.high
is_high_not_set = False
if 'fd_step_type' in meta:
self.step_type_custom[j] = meta['fd_step_type']
step_type = self.step_type_custom[j]
else:
step_type = self.step_type
# Bounds scaled
if step_type == 'bounds_scaled':
if low is None and high is None:
raise RuntimeError("For variable '%s', a finite "
"difference step type of bounds_scaled "
"is used but required low and "
"high values are not set" % srcs[0])
if low == - float_info.max:
raise RuntimeError("For variable '%s', a finite "
"difference step type of "
"bounds_scaled is used but required "
"low value is not set" % srcs[0])
if high == float_info.max:
raise RuntimeError("For variable '%s', a finite "
"difference step type of "
"bounds_scaled is used but required "
"high value is not set" % srcs[0])
self.fd_step[j] = (high - low) * self.fd_step[j]
if 'fd_form' in meta:
self.form_custom[j] = meta['fd_form']
val = self.scope.get(srcs[0])
width = flattened_size(srcs[0], val, self.scope)
for src in srcs:
self.in_bounds[src] = (in_size, in_size+width)
in_size += width
self.high[j] = high
self.low[j] = low
out_size = 0
for src in self.outputs:
val = self.scope.get(src)
width = flattened_size(src, val)
out_size += width
# Size our Jacobian
if return_format == 'dict':
self.J = {}
for okey in outputs:
self.J[okey] = {}
for ikey in inputs:
if isinstance(ikey, tuple):
ikey = ikey[0]
# If output not on this process, just allocate a dummy
# array
if MPI and okey not in self.system.vec['u']:
osize = 0
else:
osize = self.system.vec['u'][okey].size
isize = self.system.vec['p'][ikey].size
self.J[okey][ikey] = zeros((osize, isize))
else:
self.J = zeros((out_size, in_size))
self.y_base = zeros((out_size,))
self.y = zeros((out_size,))
self.y2 = zeros((out_size,))
def __init__(self, pa):
""" Performs finite difference on the components in a given
pseudo_assembly. """
self.inputs = pa.inputs
self.outputs = pa.outputs
self.in_bounds = {}
self.out_bounds = {}
self.pa = pa
self.scope = pa.wflow.scope
options = pa.wflow._parent.gradient_options
self.fd_step = options.fd_step*ones((len(self.inputs)))
self.form = options.fd_form
self.form_custom = {}
self.step_type = options.fd_step_type
self.step_type_custom = {}
self.relative_threshold = 1.0e-4
driver = self.pa.wflow._parent
driver_params = []
driver_targets = []
if hasattr(driver, 'get_parameters'):
driver_params = self.pa.wflow._parent.get_parameters()
driver_targets = driver.list_param_targets()
in_size = 0
for j, srcs in enumerate(self.inputs):
# Support for parameter groups
if isinstance(srcs, basestring):
srcs = [srcs]
# Local stepsize support
meta = self.scope.get_metadata(self.scope._depgraph.base_var(srcs[0]))
if 'fd_step' in meta:
self.fd_step[j] = meta['fd_step']
if srcs[0] in driver_targets:
if srcs[0] in driver_params:
param = driver_params[srcs[0]]
if param.fd_step is not None:
self.fd_step[j] = param.fd_step
else:
# have to check through all the param groups
for param_group in driver_params:
if not isinstance(param_group, str) and \
srcs[0] in param_group:
param = driver_params[param_group]
if param.fd_step is not None:
self.fd_step[j] = param.fd_step
break
if 'fd_step_type' in meta:
self.step_type_custom[j] = meta['fd_step_type']
if 'fd_form' in meta:
self.form_custom[j] = meta['fd_form']
val = self.scope.get(srcs[0])
width = flattened_size(srcs[0], val, self.scope)
for src in srcs:
self.in_bounds[src] = (in_size, in_size+width)
in_size += width
out_size = 0
for src in self.outputs:
val = self.scope.get(src)
width = flattened_size(src, val)
self.out_bounds[src] = (out_size, out_size+width)
out_size += width
self.J = zeros((out_size, in_size))
self.y_base = zeros((out_size,))
self.x = zeros((in_size,))
self.y = zeros((out_size,))
self.y2 = zeros((out_size,))
def initialize_residual(self):
"""Creates the array that stores the residual. Also returns the
number of edges.
"""
dgraph = self.derivative_graph()
if 'mapped_inputs' in dgraph.graph:
inputs = dgraph.graph['mapped_inputs']
else:
inputs = dgraph.graph['inputs']
basevars = set()
edges = self.edge_list()
implicit_edges = self.get_implicit_info()
sortedkeys = sorted(implicit_edges)
sortedkeys.extend(sorted(edges.keys()))
nEdge = 0
for src in sortedkeys:
if src in implicit_edges:
targets = implicit_edges[src]
is_implicit = True
else:
targets = edges[src]
is_implicit = False
if isinstance(targets, str):
targets = [targets]
# Implicit source edges are tuples.
if is_implicit == True:
impli_edge = nEdge
for resid in src:
unmap_src = from_PA_var(resid)
val = self.scope.get(unmap_src)
width = flattened_size(unmap_src, val, self.scope)
if isinstance(val, ndarray):
shape = val.shape
else:
shape = 1
bound = (impli_edge, impli_edge+width)
self.set_bounds(resid, bound)
basevars.add(resid)
impli_edge += width
# Regular components
else:
# Only need to grab the source (or first target for param) to
# figure out the size for the residual vector
measure_src = src
if '@in' in src:
idx = int(src[3:].split('[')[0])
inp = inputs[idx]
if not isinstance(inp, basestring):
inp = inp[0]
if inp in dgraph:
measure_src = inp
else:
measure_src = targets[0]
elif src == '@fake':
for t in targets:
if not t.startswith('@'):
measure_src = t
break
else:
raise RuntimeError("malformed graph!")
# Find our width, etc.
unmap_src = from_PA_var(measure_src)
val = self.scope.get(unmap_src)
width = flattened_size(unmap_src, val, self.scope)
if isinstance(val, ndarray):
shape = val.shape
else:
shape = 1
# Special poke for boundary node
if is_boundary_node(dgraph, measure_src) or \
is_boundary_node(dgraph, dgraph.base_var(measure_src)):
bound = (nEdge, nEdge+width)
self.set_bounds(measure_src, bound)
src_noidx = src.split('[', 1)[0]
# Poke our source data
# Array slice of src that is already allocated
if '[' in src and src_noidx in basevars:
_, _, idx = src.partition('[')
basebound = self.get_bounds(src_noidx)
if not '@in' in src_noidx:
unmap_src = from_PA_var(src_noidx)
val = self.scope.get(unmap_src)
shape = val.shape
offset = basebound[0]
istring, ix = flatten_slice(idx, shape, offset=offset,
name='ix')
bound = (istring, ix)
# Already allocated
width = 0
# Input-input connection to implicit state
elif src_noidx in basevars:
bound = self.get_bounds(src_noidx)
width = 0
# Normal src
else:
bound = (nEdge, nEdge+width)
self.set_bounds(src, bound)
basevars.add(src)
# Poke our target data
impli_edge = nEdge
for target in targets:
# Handle States in implicit comps
if is_implicit == True:
if isinstance(target, str):
target = [target]
unmap_targ = from_PA_var(target[0])
val = self.scope.get(unmap_targ)
imp_width = flattened_size(unmap_targ, val, self.scope)
if isinstance(val, ndarray):
shape = val.shape
else:
shape = 1
for itarget in target:
bound = (impli_edge, impli_edge+imp_width)
self.set_bounds(itarget, bound)
basevars.add(itarget)
impli_edge += imp_width
width = impli_edge - nEdge
elif not target.startswith('@'):
self.set_bounds(target, bound)
#print input_src, src, target, bound,
nEdge += width
impli_edge = nEdge
# Initialize the residual vector on the first time through, and also
# if for some reason the number of edges has changed.
if self.res is None or nEdge != self.res.shape[0]:
self.res = zeros((nEdge, 1))
return nEdge
def calc_gradient(self, inputs=None, outputs=None, upscope=False, mode='auto'):
"""Returns the gradient of the passed outputs with respect to
all passed inputs.
inputs: list of strings or tuples of strings
List of input variables that we are taking derivatives with respect
to. They must be within this workflow's scope. If no inputs are
given, the parent driver's parameters are used. A tuple can be used
to link inputs together.
outputs: list of strings
List of output variables that we are taking derivatives of.
They must be within this workflow's scope. If no outputs are
given, the parent driver's objectives and constraints are used.
upscope: boolean
This is set to True when our workflow is part of a subassembly that
lies in a workflow that needs a gradient with respect to variables
outside of this workflow, so that the caches can be reset.
mode: string
Set to 'forward' for forward mode, 'adjoint' for adjoint mode,
'fd' for full-model finite difference (with fake finite
difference disabled), or 'auto' to let OpenMDAO determine the
correct mode.
"""
self._J_cache = {}
# User may request full-model finite difference.
if self._parent.gradient_options.force_fd == True:
mode = 'fd'
# This function can be called from a parent driver's workflow for
# assembly recursion. We have to clear our cache if that happens.
# We also have to clear it next time we arrive back in our workflow.
if upscope or self._upscoped:
self._derivative_graph = None
self._edges = None
self._comp_edges = None
self._upscoped = upscope
dgraph = self.derivative_graph(inputs, outputs, fd=(mode == 'fd'))
if 'mapped_inputs' in dgraph.graph:
inputs = dgraph.graph['mapped_inputs']
outputs = dgraph.graph['mapped_outputs']
else:
inputs = dgraph.graph['inputs']
outputs = dgraph.graph['outputs']
n_edge = self.initialize_residual()
# cache Jacobians for comps that return them from provideJ
# Size our Jacobian
num_in = 0
for item in inputs:
# For parameter groups, only size the first
if not isinstance(item, basestring):
item = item[0]
try:
i1, i2 = self.get_bounds(item)
if isinstance(i1, list):
num_in += len(i1)
else:
num_in += i2-i1
except KeyError:
val = self.scope.get(item)
num_in += flattened_size(item, val, self.scope)
num_out = 0
for item in outputs:
try:
i1, i2 = self.get_bounds(item)
if isinstance(i1, list):
num_out += len(i1)
else:
num_out += i2-i1
except KeyError:
val = self.scope.get(item)
num_out += flattened_size(item, val, self.scope)
shape = (num_out, num_in)
# Auto-determine which mode to use based on Jacobian shape.
if mode == 'auto':
# TODO - additional determination based on presence of
# apply_derivT
if num_in > num_out:
mode = 'adjoint'
else:
mode = 'forward'
if mode == 'adjoint':
J = calc_gradient_adjoint(self, inputs, outputs, n_edge, shape)
elif mode in ['forward', 'fd']:
J = calc_gradient(self, inputs, outputs, n_edge, shape)
else:
msg = "In calc_gradient, mode must be 'forward', 'adjoint', " + \
"'auto', or 'fd', but a value of %s was given." % mode
self.scope.raise_exception(msg, RuntimeError)
# Finally, we need to untransform the jacobian if any parameters have
# scalers.
#print 'edges:', self._edges
if not hasattr(self._parent, 'get_parameters'):
return J
params = self._parent.get_parameters()
if len(params) == 0:
return J
i = 0
for group in inputs:
if isinstance(group, str):
group = [group]
name = group[0]
if len(group) > 1:
pname = tuple([from_PA_var(aname) for aname in group])
else:
pname = from_PA_var(name)
try:
i1, i2 = self.get_bounds(name)
except KeyError:
continue
if isinstance(i1, list):
width = len(i1)
else:
width = i2-i1
if pname in params:
scaler = params[pname].scaler
if scaler != 1.0:
J[:, i:i+width] = J[:, i:i+width]*scaler
i = i + width
#print J
return J
def __init__(self, pa):
""" Performs finite difference on the components in a given
pseudo_assembly. """
self.inputs = pa.inputs
self.outputs = pa.outputs
self.in_bounds = {}
self.out_bounds = {}
self.pa = pa
self.scope = pa.wflow.scope
options = pa.wflow._parent.gradient_options
self.fd_step = options.fd_step * ones((len(self.inputs)))
self.form = options.fd_form
self.form_custom = {}
self.step_type = options.fd_step_type
self.step_type_custom = {}
self.relative_threshold = 1.0e-4
driver = self.pa.wflow._parent
driver_params = []
driver_targets = []
if hasattr(driver, 'get_parameters'):
driver_params = self.pa.wflow._parent.get_parameters()
driver_targets = driver.list_param_targets()
in_size = 0
for j, srcs in enumerate(self.inputs):
low = high = None
# Support for parameter groups
if isinstance(srcs, basestring):
srcs = [srcs]
# Local stepsize support
meta = self.scope.get_metadata(
self.scope._depgraph.base_var(srcs[0]))
if 'fd_step' in meta:
self.fd_step[j] = meta['fd_step']
if 'low' in meta:
low = meta['low']
if 'high' in meta:
high = meta['high']
if srcs[0] in driver_targets:
if srcs[0] in driver_params:
param = driver_params[srcs[0]]
if param.fd_step is not None:
self.fd_step[j] = param.fd_step
if param.low is not None:
low = param.low
if param.high is not None:
high = param.high
else:
# have to check through all the param groups
for param_group in driver_params:
is_fd_step_not_set = is_low_not_set = is_high_not_set = True
if not isinstance(param_group, str) and \
srcs[0] in param_group:
param = driver_params[param_group]
if is_fd_step_not_set and param.fd_step is not None:
self.fd_step[j] = param.fd_step
is_fd_step_not_set = False
if is_low_not_set and param.low is not None:
low = param.low
is_low_not_set = False
if is_high_not_set and param.high is not None:
high = param.high
is_high_not_set = False
if 'fd_step_type' in meta:
self.step_type_custom[j] = meta['fd_step_type']
step_type = self.step_type_custom[j]
else:
step_type = self.step_type
# Bounds scaled
if step_type == 'bounds_scaled':
if low is None and high is None:
raise RuntimeError(
"For variable '%s', a finite "
"difference step type of "
"bounds_scaled is used but required low and "
"high values are not set" % srcs[0])
if low == -float_info.max:
raise RuntimeError("For variable '%s', a finite "
"difference step type of "
"bounds_scaled is used but required "
"low value is not set" % srcs[0])
if high == float_info.max:
raise RuntimeError("For variable '%s', a finite "
"difference step type of "
"bounds_scaled is used but required "
"high value is not set" % srcs[0])
self.fd_step[j] = (high - low) * self.fd_step[j]
if 'fd_form' in meta:
self.form_custom[j] = meta['fd_form']
val = self.scope.get(srcs[0])
width = flattened_size(srcs[0], val, self.scope)
for src in srcs:
self.in_bounds[src] = (in_size, in_size + width)
in_size += width
out_size = 0
for src in self.outputs:
val = self.scope.get(src)
width = flattened_size(src, val)
self.out_bounds[src] = (out_size, out_size + width)
out_size += width
self.J = zeros((out_size, in_size))
self.y_base = zeros((out_size, ))
self.x = zeros((in_size, ))
self.y = zeros((out_size, ))
self.y2 = zeros((out_size, ))
