From ca41d9ccd8ed00e9efa20bc104e21fc0e49a301d Mon Sep 17 00:00:00 2001
From: Paul Jungeblut <paul.jungeblut@gmail.com>
Date: Mon, 19 Jun 2017 15:52:34 +0200
Subject: Adding Dinic's algorithm with capacity scaling and numerical
 integration with adaptive simpson rule.

---
 math/math.tex    |  3 +++
 math/simpson.cpp | 12 ++++++++++++
 2 files changed, 15 insertions(+)
 create mode 100644 math/simpson.cpp

(limited to 'math')

diff --git a/math/math.tex b/math/math.tex
index 94adf9f..c2f5d63 100644
--- a/math/math.tex
+++ b/math/math.tex
@@ -109,6 +109,9 @@ Multipliziert Polynome $A$ und $B$.
 \end{itemize}
 \lstinputlisting{math/fft.cpp}
 
+\subsection{Numerisch Integrieren, Simpsonregel}
+\lstinputlisting{math/simpson.cpp}
+
 \subsection{3D-Kugeln}
 \lstinputlisting{math/spheres.cpp}
 
diff --git a/math/simpson.cpp b/math/simpson.cpp
new file mode 100644
index 0000000..dd887e2
--- /dev/null
+++ b/math/simpson.cpp
@@ -0,0 +1,12 @@
+double f(double x) { return x; }
+
+double simps(double a, double b) {
+  return (f(a) + 4.0 * f((a + b) / 2.0) + f(b)) * (b - a) / 6.0;
+}
+
+double integrate(double a, double b) {
+  double m = (a + b) / 2.0;
+  double l = simps(a, m), r = simps(m, b), tot = simps(a, b);
+  if (abs(l + r - tot) < EPSILON) return tot;
+  return integrate(a, m) + integrate(m, b);
+}
-- 
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