Algorithmic Differentiation in Python with Application Examples
Algorithmic Differentiation in Python with Application Examples
Algorithmic Differentiation in Python with Application Examples
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Univariate Taylor Polynomial Arithmetic (UTP) (cont.)<br />
Let f (x) = (h ◦ g)(x) = h(g(x)) be a composite function, then<br />
E D (f ) = E D (h) ◦ E D (g) .<br />
I.e. E D is a homomorphism that preserves the function composition.<br />
Therefore: Need algorithms to compute<br />
[y 0 , . . . , y D−1 ] = E D (φ)([x 0 , . . . , x D−1 ])<br />
only for the elementary functions φ ∈ {+, −, ∗, /, . . . } !<br />
Suggests implementation by function and operator overload<strong>in</strong>g, i.e.<br />
univariate Taylor polynomial (UTP) arithmetic.<br />
Sebastian F. Walter, Humboldt-Universität zu Berl<strong>in</strong> <strong>Algorithmic</strong> () <strong>Differentiation</strong> <strong>in</strong> <strong>Python</strong> <strong>with</strong> <strong>Application</strong> <strong>Examples</strong> Wednesday, 10.07.2010 15 / 27
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