AD Tutorial at the TU Berlin
AD Tutorial at the TU Berlin
AD Tutorial at the TU Berlin
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Overall Objective Function<br />
Part I: Comput<strong>at</strong>ion of J 1 and J 2<br />
J 1 [n mts, :] =<br />
√ wmts<br />
d<br />
σ nmts (x(t nmts ; s, u(t nmts ; q), q) d(p, s) (h(tnmts , x(t nmts ; s, u(t nmts ; q), p)))<br />
J 2 =<br />
d<br />
r(q, p, s)<br />
d(p, s)<br />
Part II: Numerical Linear Algebra<br />
„<br />
J T<br />
C(J 1 , J 2 ) = (I, 0) 1 J 1 J2<br />
T « −1 „ « I<br />
J 2 0 0<br />
”<br />
=<br />
“Q T 2 (Q 2J1 T J 1Q T 2 )−1 Q 2<br />
where J2 T = (QT 1 , QT 2 )(L, 0)T<br />
Comput<strong>at</strong>ional Graph<br />
[p]<br />
[h], [r] [J 1], [J 2] [C] [Φ]<br />
Φ = λ 1 (C) , max. eigenvalue<br />
[q]<br />
[s] [x 0] [x 1] [x 2] [x 3] [x 4] . . . [x Nmts−1] [xNmts ]<br />
st<strong>at</strong>ex(t) <strong>at</strong>measurementtimes (mts) independent/dependent variables<br />
N mts Number measurment times, σ std of a measurement, q controls, p n<strong>at</strong>ure given parameter, s<br />
pseudo-Parameter (e.g. initial values), u control functions<br />
Sebastian F. Walter, HU <strong>Berlin</strong> () Not So Short <strong>Tutorial</strong> OnAlgorithmic Differenti<strong>at</strong>ion Wednesday, 04.06.2010 20 / 39
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