Added blank line to autodiff cookbook to trigger an enumeration

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George Necula 2020-02-17 16:01:10 +01:00 committed by GitHub
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@ -1399,6 +1399,7 @@
},
"source": [
"This convention covers three important cases:\n",
"\n",
"1. If `f` evaluates a holomorphic function, then we get the usual complex derivative, since $\\partial_0 u = \\partial_1 v$ and $\\partial_1 u = - \\partial_0 v$.\n",
"2. If `f` is evaluates the real-valued loss function of a complex parameter `x`, then we get a result that we can use in gradient-based optimization by taking steps in the direction of the conjugate of `grad(f)(x)`.\n",
"3. If `f` evaluates a real-to-real function, but its implementation uses complex primitives internally (some of which must be non-holomorphic, e.g. FFTs used in convolutions) then we get the same result that an implementation that only used real primitives would have given.\n",