From 327acffd33add74be825d09d672e7ac878a3eced Mon Sep 17 00:00:00 2001
From: Martin Bauer <martin.bauer@fau.de>
Date: Fri, 16 Mar 2018 12:20:13 +0100
Subject: [PATCH] Phase field tutorials + small changes in functional
derivative code
---
derivative.py | 18 ++++++++++--------
plot2d.py | 6 ++++++
2 files changed, 16 insertions(+), 8 deletions(-)
diff --git a/derivative.py b/derivative.py
index fca807113..75db20b5e 100644
--- a/derivative.py
+++ b/derivative.py
@@ -16,6 +16,7 @@ class Diff(sp.Expr):
"""
is_number = False
is_Rational = False
+ _diff_wrt = True
def __new__(cls, argument, target=-1, superscript=-1, **kwargs):
if argument == 0:
@@ -142,7 +143,7 @@ class DiffOperator(sp.Expr):
return result
@staticmethod
- def apply(expr, argument):
+ def apply(expr, argument, applyToConstants=True):
"""
Returns a new expression where each 'DiffOperator' is replaced by a 'Diff' node.
Multiplications of 'DiffOperator's are interpreted as nested application of differentiation:
@@ -152,7 +153,7 @@ class DiffOperator(sp.Expr):
args = normalizeProduct(mul)
diffs = [a for a in args if isinstance(a, DiffOperator)]
if len(diffs) == 0:
- return mul * argument
+ return mul * argument if applyToConstants else mul
rest = [a for a in args if not isinstance(a, DiffOperator)]
diffs.sort(key=defaultDiffSortKey)
result = argument
@@ -166,7 +167,7 @@ class DiffOperator(sp.Expr):
elif expr.func == sp.Add:
return expr.func(*[handleMul(a) for a in expr.args])
else:
- return expr * argument
+ return expr * argument if applyToConstants else expr
# ----------------------------------------------------------------------------------------------------------------------
@@ -442,7 +443,7 @@ def evaluateDiffs(expr, var=None):
return expr.func(*newArgs) if newArgs else expr
-def functionalDerivative(functional, v, constants=None):
+def functionalDerivative(functional, v):
"""
Computes functional derivative of functional with respect to v using Euler-Lagrange equation
@@ -457,9 +458,10 @@ def functionalDerivative(functional, v, constants=None):
of the derivative terms.
"""
diffs = functional.atoms(Diff)
- nonDiffPart = functional.subs({d: sp.Dummy() for d in diffs})
-
- partialF_partialV = sp.diff(nonDiffPart, v)
+ bulkSubstitutions = {d: sp.Dummy() for d in diffs}
+ bulkSubstitutionsInverse = {v: k for k, v in bulkSubstitutions.items()}
+ nonDiffPart = functional.subs(bulkSubstitutions)
+ partialF_partialV = sp.diff(nonDiffPart, v).subs(bulkSubstitutionsInverse)
gradientPart = 0
for diffObj in diffs:
@@ -470,4 +472,4 @@ def functionalDerivative(functional, v, constants=None):
gradientPart += Diff(partialF_partialGradV, target=diffObj.target, superscript=diffObj.superscript)
result = partialF_partialV - gradientPart
- return expandUsingLinearity(result, constants=constants)
+ return result
diff --git a/plot2d.py b/plot2d.py
index 43ba8af8b..9fc234ab7 100644
--- a/plot2d.py
+++ b/plot2d.py
@@ -84,6 +84,12 @@ def multipleScalarFields(field, **kwargs):
colorbar()
+def sympyFunction(f, var, bounds, **kwargs):
+ import sympy as sp
+ xArr = np.linspace(bounds[0], bounds[1], 101)
+ yArr = sp.lambdify(var, f)(xArr)
+ plot(xArr, yArr, **kwargs)
+
# ------------------------------------------- Animations ---------------------------------------------------------------
--
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