"In NIFTy, users can add hand-crafted point-wise nonlinearities that are then available for `Field`, `MultiField`, `Linearization` and `Operator`. This guide illustrates how this is done.\n",
"\n",
"Suppose that we would like to use the point-wise function f(x) = x*exp(x) in an operator chain. This function is called \"myptw\" in the following. We introduce this function to NIFTy by implementing two functions.\n",
"\n",
"First, one that takes a `numpy.ndarray` as an input, applies the point-wise mapping and returns the result as a `numpy.ndarray` of the same shape. Second, a function that takes a `numpy.ndarray` as an input and returns two `numpy.ndarray`s: the application of the nonlinearity (same as before) and the derivative."
]
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"def func(x):\n",
" return x*np.exp(x)\n",
"\n",
"\n",
"def func_and_derv(x):\n",
" expx = np.exp(x)\n",
" return x*expx, (1+x)*expx"
]
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"These two functions are then added to the NIFTy-internal dictionary that contains all implemented point-wise nonlinearities."
"Please remember to always check that the gradient has been implemented correctly by comparing it to an approximation to the gradient by finite differences."
