Add gradient tests

test/test_linearization.py

+# 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
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# 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 <http://www.gnu.org/licenses/>.
+#
+# Copyright(C) 2013-2019 Max-Planck-Society
+#
+# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
+
+import numpy as np
+import pytest
+from numpy.testing import assert_, assert_allclose
+
+import nifty5 as ift
+
+pmp = pytest.mark.parametrize
+
+
+def _lin2grad(lin):
+    return lin.jac(ift.full(lin.domain, 1.)).local_data
+
+
+def jt(lin, check):
+    assert_allclose(_lin2grad(lin), check)
+
+
+def test_lin():
+    dom = ift.UnstructuredDomain((1,))
+    f = ift.full(dom, 2.4)
+    var = ift.Linearization.make_var(f)
+    s = f.local_data
+
+    jt(var.exp(), np.exp(s))
+    jt(var.clip(0, 10), np.ones_like(s))
+    jt(var.clip(-1, 0), np.zeros_like(s))
+    jt(var.sqrt(), .5/np.sqrt(s))
+    jt(var.sin(), np.cos(s))
+    jt(var.cos(), -np.sin(s))
+    jt(var.tan(), 1/np.cos(s)**2)
+    jt(var.sinc(), (np.cos(np.pi*s) - np.sinc(s))/s)
+    jt(var.log(), 1/s)
+    jt(var.sinh(), np.cosh(s))
+    jt(var.cosh(), np.sinh(s))
+    jt(var.tanh(), 1 - np.tanh(s)**2)
+    jt(var.absolute(), np.ones_like(s))
+    jt(var.one_over(), -1/s**2)
+
+    sigmoid = 0.5*(1 + var.tanh())
+    jt(var.sigmoid(), sigmoid.jac(ift.full(sigmoid.domain, 1.)).local_data)
+
+    assert_allclose(
+        _lin2grad(ift.Linearization.make_var(0*f).sinc()), np.zeros(s.shape))
+    assert_(np.isnan(_lin2grad(ift.Linearization.make_var(0*f).absolute())))
+    assert_allclose(
+        _lin2grad(ift.Linearization.make_var(0*f + 10).absolute()),
+        np.ones(s.shape))
+    assert_allclose(
+        _lin2grad(ift.Linearization.make_var(0*f - 10).absolute()),
+        -np.ones(s.shape))
+
+
+@pmp('f', [
+    'log', 'exp', 'sqrt', 'sin', 'cos', 'tan', 'sinc', 'sinh', 'cosh', 'tanh',
+    'absolute', 'one_over', 'sigmoid'
+])
+def test_actual_gradients(f):
+    dom = ift.UnstructuredDomain((1,))
+    fld = ift.full(dom, 2.4)
+    eps = 1e-8
+    var0 = ift.Linearization.make_var(fld)
+    var1 = ift.Linearization.make_var(fld + eps)
+    f0 = getattr(var0, f)().val.local_data
+    f1 = getattr(var1, f)().val.local_data
+    df0 = (f1 - f0)/eps
+    df1 = _lin2grad(getattr(var0, f)())
+    assert_allclose(df0, df1, rtol=100*eps)