def _eval_fd(self, expr):
expr = getattr(expr, 'evaluate', expr)
if self.side in [left, right] and self.deriv_order == 1:
res = first_derivative(expr,
self.dims[0],
self.fd_order,
side=self.side,
matvec=self.transpose,
x0=self.x0)
elif len(self.dims) > 1:
res = cross_derivative(expr,
self.dims,
self.fd_order,
self.deriv_order,
matvec=self.transpose,
x0=self.x0)
else:
res = generic_derivative(expr,
*self.dims,
self.fd_order,
self.deriv_order,
matvec=self.transpose,
x0=self.x0)
for e in self._subs:
res = res.xreplace(e)
return res
def _eval_fd(self, expr):
"""
Evaluate finite difference approximation of the Derivative.
Evaluation is carried out via the following four steps:
- 1: Evaluate derivatives within the expression. For example given
`f.dx * g`, `f.dx` will be evaluated first.
- 2: Evaluate the finite difference for the (new) expression.
- 3: Evaluate remaining terms (as `g` may need to be evaluated
at a different point).
- 4: Apply substitutions.
"""
# Step 1: Evaluate derivatives within expression
expr = getattr(expr, '_eval_deriv', expr)
# Step 2: Evaluate FD of the new expression
if self.side is not None and self.deriv_order == 1:
res = first_derivative(expr, self.dims[0], self.fd_order,
side=self.side, matvec=self.transpose,
x0=self.x0)
elif len(self.dims) > 1:
res = cross_derivative(expr, self.dims, self.fd_order, self.deriv_order,
matvec=self.transpose, x0=self.x0)
else:
res = generic_derivative(expr, *self.dims, self.fd_order, self.deriv_order,
matvec=self.transpose, x0=self.x0)
# Step 3: Evaluate remaining part of expression
res = res.evaluate
# Step 4: Apply substitution
for e in self._subs:
res = res.xreplace(e)
return res
def _eval_fd(self, expr):
"""
Evaluate finite difference approximation of the Derivative.
Evaluation is carried out via the following four steps:
- 1: Evaluate derivatives within the expression. For example given
`f.dx * g`, `f.dx` will be evaluated first.
- 2: Evaluate the finite difference for the (new) expression.
- 3: Evaluate remaining terms (as `g` may need to be evaluated
at a different point).
- 4: Apply substitutions.
- 5: Cast to an object of type `EvalDiffDerivative` so that we know
the argument stems from a `Derivative. This may be useful for
later compilation passes.
"""
# Step 1: Evaluate derivatives within expression
expr = getattr(expr, '_eval_deriv', expr)
# Step 2: Evaluate FD of the new expression
if self.side is not None and self.deriv_order == 1:
res = first_derivative(expr,
self.dims[0],
self.fd_order,
side=self.side,
matvec=self.transpose,
x0=self.x0)
elif len(self.dims) > 1:
res = cross_derivative(expr,
self.dims,
self.fd_order,
self.deriv_order,
matvec=self.transpose,
x0=self.x0)
else:
res = generic_derivative(expr,
*self.dims,
self.fd_order,
self.deriv_order,
matvec=self.transpose,
x0=self.x0)
# Step 3: Evaluate remaining part of expression
res = res.evaluate
# Step 4: Apply substitution
for e in self._subs:
res = res.xreplace(e)
# Step 5: Cast to EvaluatedDerivative
assert res.is_Add
res = EvalDiffDerivative(*res.args, evaluate=False)
return res
def evaluate(self):
expr = getattr(self.expr, 'evaluate', self.expr)
if self.side in [left, right] and self.deriv_order == 1:
res = first_derivative(expr, self.dims[0], self.fd_order,
side=self.side, matvec=self.transpose)
elif len(self.dims) > 1:
res = cross_derivative(expr, self.dims, self.fd_order, self.deriv_order,
matvec=self.transpose, stagger=self.stagger)
else:
res = generic_derivative(expr, *self.dims, self.fd_order,
self.deriv_order, stagger=self.stagger[0],
matvec=self.transpose)
for e in self._eval_at:
res = res.xreplace(e)
return res
def _eval_fd(self, expr):
"""
Evaluate the finite-difference approximation of the Derivative.
Evaluation is carried out via the following three steps:
- 1: Evaluate derivatives within the expression. For example given
`f.dx * g`, `f.dx` will be evaluated first.
- 2: Evaluate the finite difference for the (new) expression.
This in turn is a two-step procedure, for Functions that may
may need to be evaluated at a different point due to e.g. a
shited derivative.
- 3: Apply substitutions.
"""
# Step 1: Evaluate derivatives within expression
try:
expr = expr._eval_deriv
except AttributeError:
pass
# Step 2: Evaluate FD of the new expression
if self.side is not None and self.deriv_order == 1:
res = first_derivative(expr,
self.dims[0],
self.fd_order,
side=self.side,
matvec=self.transpose,
x0=self.x0)
elif len(self.dims) > 1:
res = cross_derivative(expr,
self.dims,
self.fd_order,
self.deriv_order,
matvec=self.transpose,
x0=self.x0)
else:
res = generic_derivative(expr,
*self.dims,
self.fd_order,
self.deriv_order,
matvec=self.transpose,
x0=self.x0)
# Step 3: Apply substitutions
for e in self._ppsubs:
res = res.xreplace(e)
return res