"""
Define functions and objects common to the ExplicitFuncComp and ImplicitFuncComp classes.
"""
import sys
import traceback
import re
from functools import partial
from collections.abc import Iterable
import numpy as np
try:
import jax
from jax import vmap
import jax.numpy as jnp
# linear_util moved to jax.extend in jax 0.4.17, previous location is deprecated
try:
from jax.extend import linear_util
except ImportError:
from jax import linear_util
from jax.api_util import argnums_partial
from jax._src.api import _jvp, _vjp
jax.config.update("jax_enable_x64", True) # jax by default uses 32 bit floats
except Exception:
_, err, tb = sys.exc_info()
if not isinstance(err, ImportError):
traceback.print_tb(tb)
jax = None
# regex to check for variable names.
namecheck_rgx = re.compile('[_a-zA-Z][_a-zA-Z0-9]*')
# Names that are not allowed for input or output variables (keywords for options)
_disallowed_varnames = {
'units', 'shape', 'shape_by_conn', 'run_root_only', 'distributed', 'assembled_jac_type'
}
def _copy_with_ignore(dct, keep, ignore=()):
"""
Copy the entries in the given dict whose keys are in keep.
Parameters
----------
dct : dict
The dictionary to be copied.
keep : set-like
Set of keys for entries we want to keep.
ignore : set or tuple
Don't issue a warning for these non-keeper keys.
Returns
-------
dict
A new dict containing 'keep' entries.
"""
return {k: v for k, v in dct.items() if k in keep and k not in ignore}
def _check_var_name(comp, name):
match = namecheck_rgx.match(name)
if match is None or match.group() != name:
raise NameError(f"{comp.msginfo}: '{name}' is not a valid variable name.")
if name in _disallowed_varnames:
raise NameError(f"{comp.msginfo}: cannot use variable name '{name}' because "
"it's a reserved keyword.")
[docs]def jac_forward(fun, argnums, tangents):
"""
Similar to the jax.jacfwd function but allows specification of the tangent matrix.
This allows us to generate a compressed jacobian based on coloring.
Parameters
----------
fun : function
The function to be differentiated.
argnums : tuple of int or None
Specifies which positional args are dynamic. None means all positional args are dynamic.
tangents : ndarray
Array of 1.0's and 0's that is used to compute the value of the jacobian matrix.
Returns
-------
function
If there are multiple output variables, returns a function that returns rows of the
jacobian grouped by output variable, e.g., if there were 2 output variables of size 3 and 4,
the function would return a list with two entries. The first entry would contain the first 3
rows of J and the second would contain the next 4 rows of J. If there is only 1 output
variable, the values returned are grouped by input variable.
"""
f = linear_util.wrap_init(fun)
if argnums is None:
def jacfunf(*args):
return vmap(partial(_jvp, f, args), out_axes=(None, -1))(tangents)[1]
else:
def jacfunf(*args):
f_partial, dyn_args = argnums_partial(f, argnums, args)
return vmap(partial(_jvp, f_partial, dyn_args), out_axes=(None, -1))(tangents)[1]
return jacfunf
[docs]def jac_reverse(fun, argnums, tangents):
"""
Similar to the jax.jacrev function but allows specification of the tangent matrix.
This allows us to generate a compressed jacobian based on coloring.
Parameters
----------
fun : function
The function to be differentiated.
argnums : tuple of int or None
Specifies which positional args are dynamic. None means all positional args are dynamic.
tangents : ndarray
Array of 1.0's and 0's that is used to compute the value of the jacobian matrix.
Returns
-------
function
A function that returns rows of the jacobian grouped by function input variable, e.g., if
there were 3 input variables of size 5 and 7 and 9, the function
would return a list with 3 entries. The first entry would contain the first 5 columns of J,
the second the next 7 columns of J, and the third the next 9 columns of J. Note that for
implicit systems, the function inputs will contain both inputs and outputs in the context
of OpenMDAO.
"""
f = linear_util.wrap_init(fun)
if argnums is None:
def jacfunr(*args):
return vmap(_vjp(f, *args)[1])(tangents)
else:
def jacfunr(*args):
f_partial, dyn_args = argnums_partial(f, argnums, args)
return vmap(_vjp(f_partial, *dyn_args)[1])(tangents)
return jacfunr
[docs]def jacvec_prod(fun, argnums, invals, tangent):
"""
Similar to the jvp function but gives back a flat column.
Note: this is significantly slower (when producing a full jacobian) than jac_forward.
Parameters
----------
fun : function
The function to be differentiated.
argnums : tuple of int or None
Specifies which positional args are dynamic. None means all positional args are dynamic.
invals : tuple of float or ndarray
Dynamic function input values.
tangent : ndarray
Array of 1.0's and 0's that is used to compute a column of the jacobian matrix.
Returns
-------
function
A function to compute the jacobian vector product.
"""
f = linear_util.wrap_init(fun)
if argnums is not None:
invals = list(argnums_partial(f, argnums, invals)[1])
# compute shaped tangents to use later
sizes = np.array([jnp.size(a) for a in invals])
inds = np.cumsum(sizes[:-1])
shaped_tangents = [a.reshape(s.shape) for a, s in zip(np.split(tangent, inds, axis=0), invals)]
if argnums is None:
def jvfun(inps):
return _jvp(f, inps, shaped_tangents)[1]
else:
def jvfun(inps):
f_partial, dyn_args = argnums_partial(f, argnums, inps)
return _jvp(f_partial, list(dyn_args), shaped_tangents)[1]
return jvfun
def _get_tangents(vals, direction, coloring=None, argnums=None, trans=None):
"""
Return a tuple of tangents values for use with vmap.
Parameters
----------
vals : list
List of function input values.
direction : str
Derivative computation direction ('fwd' or 'rev').
coloring : Coloring or None
If not None, the Coloring object used to compute a compressed tangent array.
argnums : list of int or None
Indices of dynamic (differentiable) function args.
trans : ndarray
Translation array from jacobian indices into function arg indices. This is needed
because OpenMDAO expects ordering to be outputs first, then inputs, but function args
could be in any order.
Returns
-------
tuple of ndarray or ndarray
The tangents values to be passed to vmap.
"""
if argnums is None:
leaves = vals
else:
leaves = [vals[i] for i in argnums]
sizes = [np.size(a) for a in leaves]
inds = np.cumsum(sizes[:-1])
if coloring is None:
tangent = np.eye(np.sum(sizes))
if trans is not None:
tangent = tangent[:, trans]
else:
tangent = coloring.tangent_matrix(direction, trans=trans)
shapes = [tangent.shape[:1] + np.shape(v) for v in leaves]
tangents = tuple([np.reshape(a, shp) for a, shp in zip(np.split(tangent, inds, axis=1),
shapes)])
if len(leaves) == 1:
tangents = tangents[0]
return tangents
def _ensure_iter(val):
"""
Turn the given value into an iterator if it is not already.
Parameters
----------
val : object
The value to be iterated over.
Returns
-------
tuple or iterable
"""
if isinstance(val, Iterable):
return val
return val,
