From 807ee8b1fd393b05bdd814760f34003ce9d3de41 Mon Sep 17 00:00:00 2001
From: Martin Bauer <martin.bauer@fau.de>
Date: Tue, 7 Aug 2018 14:15:30 +0200
Subject: [PATCH] Generalized N phases model: bulk functions f1 and f2 can be
changed from outside
---
sympyextensions.py | 24 ++++++++++++++++++++++++
1 file changed, 24 insertions(+)
diff --git a/sympyextensions.py b/sympyextensions.py
index 71fc975a8..51a2f77e2 100644
--- a/sympyextensions.py
+++ b/sympyextensions.py
@@ -55,6 +55,30 @@ def kronecker_delta(*args):
return 1
+def tanh_step_function_approximation(x, step_location, kind='right', steepness=0.0001):
+ """Approximation of step function by a tanh function
+
+ >>> tanh_step_function_approximation(1.2, step_location=1.0, kind='right')
+ 1.00000000000000
+ >>> tanh_step_function_approximation(0.9, step_location=1.0, kind='right')
+ 0
+ >>> tanh_step_function_approximation(1.1, step_location=1.0, kind='left')
+ 0
+ >>> tanh_step_function_approximation(0.9, step_location=1.0, kind='left')
+ 1.00000000000000
+ >>> tanh_step_function_approximation(0.5, step_location=(0, 1), kind='middle')
+ 1
+ """
+ if kind == 'left':
+ return (1 - sp.tanh((x - step_location) / steepness)) / 2
+ elif kind == 'right':
+ return (1 + sp.tanh((x - step_location) / steepness)) / 2
+ elif kind == 'middle':
+ x1, x2 = step_location
+ return 1 - (tanh_step_function_approximation(x, x1, 'left', steepness) + \
+ tanh_step_function_approximation(x, x2, 'right', steepness))
+
+
def multidimensional_sum(i, dim):
"""Multidimensional summation
--
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