def reduce_jacobian(J, i1, i2, idx, ish, o1, o2, odx, osh):
""" Return the subportion of the Jacobian that is valid for a particular
input and output slice.
J: 2D ndarray
Full Jacobian
i1, i2: int, int
Start and end index for the input variable
o1, o2: int, int
Start and end index for the output variable
idx, odx: str, str
Index strings for the input and output, if they are arrays. These
are None if the entries in the Jacobian have already sliced the
array for us (this can happen with pseudoAssemblies), in which case
we need to do no work.
ish, osh: tuples
Shapes of the original input and output variables before being
flattened.
"""
if idx or odx:
if idx: # J inputs
istring, ix = flatten_slice(idx, ish, offset=i1, name='ix')
else: # The entire array, already flat
istring = 'i1:i2'
if odx: # J Outputs
ostring, ox = flatten_slice(odx, osh, offset=o1, name='ox')
else: # The entire array, already flat
ostring = 'o1:o2'
if ':' not in ostring and len(ox) > 1:
ostring = 'vstack(%s)' % ostring
if ':' not in istring and len(ix) > 1:
istring = 'hstack(%s)' % istring
return eval('J[%s, %s]' % (ostring, istring))
else:
return J[o1:o2, i1:i2]
def reduce_jacobian(J, i1, i2, idx, ish, o1, o2, odx, osh):
""" Return the subportion of the Jacobian that is valid for a particular
input and output slice.
J: 2D ndarray
Full Jacobian
i1, i2: int, int
Start and end index for the input variable
o1, o2: int, int
Start and end index for the output variable
idx, odx: str, str
Index strings for the input and output, if they are arrays. These
are None if the entries in the Jacobian have already sliced the
array for us (this can happen with pseudoAssemblies), in which case
we need to do no work.
ish, osh: tuples
Shapes of the original input and output variables before being
flattened.
"""
if idx or odx:
if idx: # J inputs
istring, ix = flatten_slice(idx, ish, offset=i1, name='ix')
else: # The entire array, already flat
istring = 'i1:i2'
if odx: # J Outputs
ostring, ox = flatten_slice(odx, osh, offset=o1, name='ox')
else: # The entire array, already flat
ostring = 'o1:o2'
if ':' not in ostring and len(ox) > 1:
ostring = 'vstack(%s)' % ostring
if ':' not in istring and len(ix) > 1:
istring = 'hstack(%s)' % istring
return eval('J[%s, %s]' % (ostring, istring))
else:
return J[o1:o2, i1:i2]
def test_general_flatten_slice(self):
# Test capability to flatten any slice.
shape = (5,)
index = "[1]"
flat_str, ii = flatten_slice(index, shape, name="ii")
self.assertTrue(flat_str == "ii:ii+1")
self.assertEqual(ii, 1)
shape = (3, 4)
index = "[1, 2]"
flat_str, ii = flatten_slice(index, shape, name="ii")
self.assertTrue(flat_str == "ii:ii+1")
self.assertEqual(ii, 6)
shape = (9, 7)
index = "[-1, -1]"
flat_str, ii = flatten_slice(index, shape, name="ii")
self.assertTrue(flat_str == "ii")
self.assertEqual(ii, 62)
shape = (4, 7)
index = "[:, 3]"
flat_str, ii = flatten_slice(index, shape, name="ii")
self.assertTrue(flat_str == "ii")
self.assertTrue(set(ii) == set([3, 10, 17, 24]))
shape = (50,)
index = "[-2]"
flat_str, ii = flatten_slice(index, shape, name="ii")
self.assertTrue(flat_str == "ii")
self.assertEqual(ii, 48)
shape = (50,)
index = "[3:-3:5]"
flat_str, ii = flatten_slice(index, shape, name="ii")
self.assertTrue(flat_str == "ii")
self.assertTrue(set(ii) == set([3, 8, 13, 18, 23, 28, 33, 38, 43]))
def test_general_flatten_slice(self):
# Test capability to flatten any slice.
shape = (5, )
index = '[1]'
flat_str, ii = flatten_slice(index, shape, name='ii')
self.assertTrue(flat_str == 'ii:ii+1')
self.assertEqual(ii, 1)
shape = (3, 4)
index = '[1, 2]'
flat_str, ii = flatten_slice(index, shape, name='ii')
self.assertTrue(flat_str == 'ii:ii+1')
self.assertEqual(ii, 6)
shape = (9, 7)
index = '[-1, -1]'
flat_str, ii = flatten_slice(index, shape, name='ii')
self.assertTrue(flat_str == 'ii')
self.assertEqual(ii, 62)
shape = (4, 7)
index = '[:, 3]'
flat_str, ii = flatten_slice(index, shape, name='ii')
self.assertTrue(flat_str == 'ii')
self.assertTrue(set(ii) == set([3, 10, 17, 24]))
shape = (50, )
index = '[-2]'
flat_str, ii = flatten_slice(index, shape, name='ii')
self.assertTrue(flat_str == 'ii')
self.assertEqual(ii, 48)
shape = (50, )
index = '[3:-3:5]'
flat_str, ii = flatten_slice(index, shape, name='ii')
self.assertTrue(flat_str == 'ii')
self.assertTrue(set(ii) == set([3, 8, 13, 18, 23, 28, 33, 38, 43]))
def test_general_flatten_slice(self):
shape = (5,)
index = '[1]'
flat_str, ii = flatten_slice(index, shape, name='ii')
self.assertTrue(flat_str=='ii:ii+1')
self.assertEqual(ii, 1)
shape = (3, 4)
index = '[1, 2]'
flat_str, ii = flatten_slice(index, shape, name='ii')
self.assertTrue(flat_str=='ii:ii+1')
self.assertEqual(ii, 6)
shape = (9, 7)
index = '[-1, -1]'
flat_str, ii = flatten_slice(index, shape, name='ii')
self.assertTrue(flat_str=='ii')
self.assertEqual(ii, 62)
shape = (4, 7)
index = '[:, 3]'
flat_str, ii = flatten_slice(index, shape, name='ii')
self.assertTrue(flat_str=='ii')
self.assertTrue(set(ii)==set([3, 10, 17, 24]))
shape = (50,)
index = '[-2]'
flat_str, ii = flatten_slice(index, shape, name='ii')
self.assertTrue(flat_str=='ii')
self.assertEqual(ii, 48)
shape = (50,)
index = '[3:-3:5]'
flat_str, ii = flatten_slice(index, shape, name='ii')
self.assertTrue(flat_str=='ii')
self.assertTrue(set(ii)==set([3, 8, 13, 18, 23, 28, 33, 38, 43]))
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 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