From 1bd1c6d6568c5c48ea376ce418ef43aa64b7ea31 Mon Sep 17 00:00:00 2001
From: Martin Bauer <martin.bauer@fau.de>
Date: Fri, 29 Mar 2019 13:27:24 +0100
Subject: [PATCH] pystencils, new feature: placeholder functions
---
pystencils/placeholder_function.py | 71 ++++++++++++++++++++++++++++++
1 file changed, 71 insertions(+)
create mode 100644 pystencils/placeholder_function.py
diff --git a/pystencils/placeholder_function.py b/pystencils/placeholder_function.py
new file mode 100644
index 0000000..73d8bda
--- /dev/null
+++ b/pystencils/placeholder_function.py
@@ -0,0 +1,71 @@
+import sympy as sp
+from typing import List
+from pystencils.assignment import Assignment
+from pystencils.transformations import generic_visit
+
+
+class PlaceholderFunction:
+ pass
+
+
+def to_placeholder_function(expr, name):
+ """Replaces an expression by a sympy function.
+
+ - replacing an expression with just a symbol would lead to problem when calculating derivatives
+ - placeholder functions get rid of this problem
+
+ Examples:
+ >>> x, t = sp.symbols("x, t")
+ >>> temperature = x**2 + t**4 # some 'complicated' dependency
+ >>> temperature_placeholder = to_placeholder_function(temperature, 'T')
+ >>> diffusivity = temperature_placeholder + 42 * t
+ >>> sp.diff(diffusivity, t) # returns a symbol instead of the computed derivative
+ _dT_dt + 42
+ >>> result, subexpr = remove_placeholder_functions(diffusivity)
+ >>> result
+ T + 42*t
+ >>> subexpr
+ [Assignment(T, t**4 + x**2), Assignment(_dT_dt, 4*t**3), Assignment(_dT_dx, 2*x)]
+
+ """
+ symbols = list(expr.atoms(sp.Symbol))
+ symbols.sort(key=lambda e: e.name)
+ derivative_symbols = [sp.Symbol("_d{}_d{}".format(name, s.name)) for s in symbols]
+ derivatives = [sp.diff(expr, s) for s in symbols]
+
+ assignments = [Assignment(sp.Symbol(name), expr)]
+ assignments += [Assignment(symbol, derivative)
+ for symbol, derivative in zip(derivative_symbols, derivatives)
+ if not derivative.is_constant()]
+
+ def fdiff(_, index):
+ result = derivatives[index - 1]
+ return result if result.is_constant() else derivative_symbols[index - 1]
+
+ func = type(name, (sp.Function, PlaceholderFunction),
+ {'fdiff': fdiff,
+ 'value': sp.Symbol(name),
+ 'subexpressions': assignments,
+ 'nargs': len(symbols)})
+ return func(*symbols)
+
+
+def remove_placeholder_functions(expr):
+ subexpressions = []
+
+ def visit(e):
+ if isinstance(e, PlaceholderFunction):
+ for se in e.subexpressions:
+ if se.lhs not in {a.lhs for a in subexpressions}:
+ subexpressions.append(se)
+ return e.value
+ else:
+ new_args = [visit(a) for a in e.args]
+ return e.func(*new_args) if new_args else e
+
+ return generic_visit(expr, visit), subexpressions
+
+
+def prepend_placeholder_functions(assignments: List[Assignment]):
+ result, subexpressions = remove_placeholder_functions(assignments)
+ return subexpressions + result
--
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