Commit febe7090 authored by Philipp Arras's avatar Philipp Arras
Browse files

Add explanation how to add nonlinearities to NIFTy

parent 2236cf7b
Pipeline #103346 passed with stages
in 14 minutes and 10 seconds
......@@ -147,3 +147,8 @@ run_visual_vi:
stage: demo_runs
- python3 demos/
stage: demo_runs
- python3 demos/
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <>.
# Copyright(C) 2021 Max-Planck-Society
# Author: Philipp Arras
import nifty7 as ift
import numpy as np
# In NIFTy, users can add hand-crafted point-wise nonlinearities that are then
# available for `Field`, `MultiField`, `Linearization` and `Operator`. This
# guide shows an example how this is done.
# Suppose, we would like to use the function f(x) = x*exp(x) point-wise in an
# operator chain. This function is called "myptw" in the following. We
# introduce this function to NIFTy by implementing two functions.
# 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 an `numpy.ndarray` as an input and returns two
# `numpy.ndarray`s: the application of the nonlinearity (same as before) and
# the derivative.
def func(x):
return x*np.exp(x)
def func_and_derv(x):
expx = np.exp(x)
return x*expx, (1+x)*expx
# These two functions are then added to the NIFTy-internal dictionary that
# contains all implemented point-wise nonlinearities.
ift.pointwise.ptw_dict["myptw"] = func, func_and_derv
# This allows us to apply this non-linearity on `Field`s, ...
dom = ift.UnstructuredDomain(10)
fld = ift.from_random(dom)
fld = ift.full(dom, 2.)
a = fld.ptw("myptw")
b = ift.makeField(dom, func(fld.val))
ift.extra.assert_allclose(a, b)
# `MultiField`s, ...
mdom = ift.makeDomain({"bar": ift.UnstructuredDomain(10)})
mfld = ift.from_random(mdom)
a = mfld.ptw("myptw")
b = ift.makeField(mdom, {"bar": func(mfld["bar"].val)})
ift.extra.assert_allclose(a, b)
# Linearizations (including the Jacobian), ...
# (Value)
lin = ift.Linearization.make_var(fld)
a = lin.ptw("myptw").val
b = ift.makeField(dom, func(fld.val))
ift.extra.assert_allclose(a, b)
# (Jacobian)
op_a = lin.ptw("myptw").jac
op_b = ift.makeOp(ift.makeField(dom, func_and_derv(fld.val)[1]))
testing_vector = ift.from_random(dom)
# and `Operator`s.
op = ift.FieldAdapter(dom, "foo").ptw("myptw")
# We check that the gradient has been implemented correctly by comparing it to
# an approximation to the gradient by finite differences.
def check(func_name, eps=1e-7):
pos = ift.from_random(ift.UnstructuredDomain(10))
var0 = ift.Linearization.make_var(pos)
var1 = ift.Linearization.make_var(pos+eps)
df0 = (var1.ptw(func_name).val - var0.ptw(func_name).val)/eps
df1 = var0.ptw(func_name).jac(ift.full(lin.domain, 1.))
# rtol depends on how nonlinear the function is
ift.extra.assert_allclose(df0, df1, rtol=100*eps)
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