import numpy as np
from .problem_wrapper import ProblemWrapper
from iwopy.core import ProblemDefaultFunc
[docs]class LocalFD(ProblemWrapper):
"""
A wrapper that provides finite distance
differentiation by local stepwise evaluation.
Attributes
----------
order: dict
Finite difference order. Key: variable name
str, value: 1 = forward, -1 = backward, 2 = centre
orderb: dict or int
Finite difference order of boundary points.
Key: variable name str, value: order int
:group: wrappers
"""
[docs] def __init__(
self,
base_problem,
deltas,
fd_order=1,
fd_bounds_order=None,
name=None,
):
"""
Constructor
Parameters
----------
base_problem: iwopy.Problem
The underlying concrete problem
deltas: dict
The step sizes. Key: variable name str,
Value: step size. Will be adjusted to the
variable bounds if necessary.
fd_order: dict or int
Finite difference order. Either a dict with
key: variable name str, value: order int, or
a global integer order for all variables.
1 = forward, -1 = backward, 2 = centre
fd_bounds_order: dict or int
Finite difference order of boundary points.
Either a dict with key: variable name str,
value: order int, or a global integer order
for all variables. Default is same as fd_order
name: str, optional
The problem name
"""
name = base_problem.name + "_fd" if name is None else name
super().__init__(base_problem, name)
if isinstance(deltas, float):
deltas = {v: deltas for v in base_problem.var_names_float()}
self._deltas = deltas
if isinstance(fd_order, int):
self.order = {v: fd_order for v in deltas.keys()}
else:
self.order = fd_order
for v in deltas.keys():
if v not in self.order:
raise KeyError(
f"Problem '{self.name}': Missing fd_order entry for variable '{v}'"
)
if fd_bounds_order is None:
self.orderb = {v: abs(o) for v, o in self.order.items()}
elif isinstance(fd_bounds_order, int):
self.orderb = {v: fd_bounds_order for v in deltas.keys()}
else:
self.orderb = fd_bounds_order
for v in deltas.keys():
if v not in self.orderb:
raise KeyError(
f"Problem '{self.name}': Missing fd_bounds_order entry for variable '{v}'"
)
[docs] def initialize(self, verbosity=1):
"""
Initialize the problem.
Parameters
----------
verbosity: int
The verbosity level, 0 = silent
"""
super().initialize(verbosity)
self._vinds = []
self._order = []
self._orderb = []
self._d = []
vnms = list(super().var_names_float())
for v in self._deltas.keys():
if v not in vnms:
raise KeyError(
f"Problem '{self.name}': Variable '{v}' given in deltas, but not found in problem float variables {vnms}"
)
vi = vnms.index(v)
self._vinds.append(vi)
self._order.append(self.order[v])
self._orderb.append(self.orderb[v])
self._d.append(self._deltas[v])
self._order = np.array(self._order, dtype=np.int32)
self._orderb = np.array(self._orderb, dtype=np.int32)
self._d = np.array(self._d, dtype=np.float64)
sel = (self._order == -1) | (self._order == 1) | (self._order == 2)
if not np.all(sel):
raise NotImplementedError(
f"Order(s) {list(np.unique(self._order[~sel]))} not implemented."
)
sel = (self._orderb == -1) | (self._orderb == 1) | (self._orderb == 2)
if not np.all(sel):
raise NotImplementedError(
f"Boundary order(s) {list(np.unique(self._orderb[~sel]))} not implemented."
)
def _grad_coeffs(self, varsf, gvars, order, orderb):
"""
Helper function that provides gradient coeffs
"""
# prepare:
n_vars = len(gvars)
vmin = np.array(self.min_values_float(), dtype=np.float64)[gvars]
vmax = np.array(self.max_values_float(), dtype=np.float64)[gvars]
x0 = varsf
d = self._d[gvars]
xplus = np.zeros((self.n_vars_float, self.n_vars_float), dtype=np.float64)
np.fill_diagonal(xplus, d)
xplus += x0[None, :]
xminus = np.zeros((self.n_vars_float, self.n_vars_float), dtype=np.float64)
np.fill_diagonal(xminus, -d)
xminus += x0[None, :]
xminus2 = None
xplus2 = None
pts = np.zeros((n_vars, 2, self.n_vars_float), dtype=np.float64)
cfs = np.zeros((n_vars, n_vars, 2), dtype=np.float64)
cf0 = np.zeros(n_vars, dtype=np.float64)
# domain, order 1:
sel = (order == 1) & (xplus.diagonal() <= vmax)
if np.any(sel):
pts[sel, 0] = xplus[sel]
cfs[sel, sel, 0] = 1 / d[sel]
cf0[sel] = -1 / d[sel]
# right boundary, order 1:
sel = (orderb == 1) & (xplus.diagonal() > vmax)
if np.any(sel):
pts[sel, 0] = xminus[sel]
cfs[sel, sel, 0] = -1 / d[sel]
cf0[sel] = 1 / d[sel]
# domain, order -1:
sel = (order == -1) & (xminus.diagonal() >= vmin)
if np.any(sel):
pts[sel, 0] = xminus[sel]
cfs[sel, sel, 0] = -1 / d[sel]
cf0[sel] = 1 / d[sel]
# left boundary, order -1:
sel = (orderb == -1) & (xminus.diagonal() < vmin)
if np.any(sel):
pts[sel, 0] = xplus[sel]
cfs[sel, sel, 0] = 1 / d[sel]
cf0[sel] = -1 / d[sel]
# domain, order 2:
sel = (order == 2) & (xplus.diagonal() <= vmax) & (xminus.diagonal() >= vmin)
if np.any(sel):
pts[sel, 0] = xplus[sel]
pts[sel, 1] = xminus[sel]
cfs[sel, sel, 0] = 0.5 / d[sel]
cfs[sel, sel, 1] = -0.5 / d[sel]
# right boundary, order 2:
sel = (orderb == 2) & (xplus.diagonal() > vmax)
if np.any(sel):
if xminus2 is None:
xminus2 = np.zeros_like(xminus)
np.fill_diagonal(xminus2, -2 * d)
xminus2 += x0[None, :]
pts[sel, 0] = xminus[sel]
pts[sel, 1] = xminus2[sel]
cf0[sel] = 1.5 / d[sel]
cfs[sel, sel, 0] = -2 / d[sel]
cfs[sel, sel, 1] = 0.5 / d[sel]
# left boundary, order 2:
sel = (orderb == 2) & (xminus.diagonal() < vmax)
if np.any(sel):
if xplus2 is None:
xplus2 = np.zeros_like(xplus)
np.fill_diagonal(xplus2, 2 * d)
xplus2 += x0[None, :]
pts[sel, 0] = xplus[sel]
pts[sel, 1] = xplus2[sel]
cf0[sel] = -1.5 / d[sel]
cfs[sel, sel, 0] = 2 / d[sel]
cfs[sel, sel, 1] = -0.5 / d[sel]
# reduce and reorganize:
sel = np.any(np.abs(cfs) > 1e-13, axis=0)
pts = pts[sel]
cfs = cfs[:, sel]
# add centre point:
sel = np.abs(cf0) > 1e-13
if np.any(sel):
pts = np.append(pts, x0[None, :], axis=0)
cfs = np.append(cfs, cf0[:, None], axis=1)
return pts, cfs
[docs] def calc_gradients(
self,
vars_int,
vars_float,
func,
components,
ivars,
fvars,
vrs,
pop=False,
verbosity=0,
):
"""
The actual gradient calculation, not to be called directly
(call `get_gradients` instead).
Can be overloaded in derived classes, the base class only considers
analytic derivatives.
Parameters
----------
vars_int: np.array
The integer variable values, shape: (n_vars_int,)
vars_float: np.array
The float variable values, shape: (n_vars_float,)
func: iwopy.core.OptFunctionList, optional
The functions to be differentiated, or None
for a list of all objectives and all constraints
(in that order)
components: list of int, optional
The function's component selection, or None for all
ivars: list of int
The indices of the function int variables in the problem
fvars: list of int
The indices of the function float variables in the problem
vrs: list of int
The function float variable indices wrt which the
derivatives are to be calculated
pop: bool
Flag for vectorizing calculations via population
verbosity: int
The verbosity level, 0 = silent
Returns
-------
gradients: numpy.ndarray
The gradients of the functions, shape:
(n_components, n_vrs)
"""
# get analytic gradient results:
gradients = super().calc_gradients(
vars_int, vars_float, func, components, ivars, fvars, vrs, verbosity
)
# find variables and components of unsolved gradients:
gnan = np.isnan(gradients)
gvars = np.unique(np.where(np.any(gnan, axis=0))[0])
pvars = np.array(fvars)[gvars]
gvars = [vi for vi in pvars if vi in self._vinds]
ivars = [self._vinds.index(vi) for vi in gvars]
cmpnts = (
np.arange(func.n_components())
if components is None
else np.array(components)
)
cmptsi = np.unique(np.where(np.any(gnan, axis=1))[0])
fcmpts = cmpnts[cmptsi]
fcomps = fcmpts if components is not None else None
if not len(gvars) or not len(fcmpts):
return gradients
del gnan
# get gradient eval points and coeffs:
varsf = vars_float[gvars]
order = self._order[ivars]
orderb = self._orderb[ivars]
epts, coeffs = self._grad_coeffs(varsf, gvars, order, orderb)
# run the calculation:
n_pop = len(epts)
varsf = np.full((n_pop, self.n_vars_float), np.nan, dtype=np.float64)
values = np.full((n_pop, len(cmptsi)), np.nan, dtype=np.float64)
varsf[:] = vars_float[None, :]
varsf[:, gvars] = epts
if pop:
varsi = np.zeros((n_pop, self.n_vars_int), dtype=np.int32)
if self.n_vars_int:
varsi[:] = vars_int[None, :]
if isinstance(func, ProblemDefaultFunc):
os, cs = self.evaluate_population(varsi, varsf)
s = np.s_[:] if components is None else fcmpts
values[:] = np.c_[os, cs][:, s]
del os, cs, s
else:
results = self.apply_population(varsi, varsf)
values[:] = func.calc_population(varsi, varsf, results, fcomps)
del results
else:
for i, vf in enumerate(varsf):
if isinstance(func, ProblemDefaultFunc):
os, cs = self.evaluate_individual(vars_int, vf)
s = np.s_[:] if components is None else fcmpts
values[i] = np.r_[os, cs][s]
del os, cs, s
else:
results = self.apply_individual(vars_int, vf)
values[i] = func.calc_individual(vars_int, vf, results, fcomps)
del results
# recombine results:
gradients[:, gvars] = np.einsum("pc,vp->cv", values, coeffs)
return gradients