-
-
Notifications
You must be signed in to change notification settings - Fork 2k
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
- Loading branch information
Showing
4 changed files
with
60 additions
and
43 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Empty file.
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -0,0 +1,56 @@ | ||
# Copyright 2020 The PyMC Developers | ||
# | ||
# Licensed under the Apache License, Version 2.0 (the "License"); | ||
# you may not use this file except in compliance with the License. | ||
# You may obtain a copy of the License at | ||
# | ||
# http://www.apache.org/licenses/LICENSE-2.0 | ||
# | ||
# Unless required by applicable law or agreed to in writing, software | ||
# distributed under the License is distributed on an "AS IS" BASIS, | ||
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | ||
# See the License for the specific language governing permissions and | ||
# limitations under the License. | ||
|
||
import numpy as np | ||
import scipy.integrate as ode | ||
|
||
from pymc.ode.utils import augment_system | ||
|
||
|
||
def test_gradients(): | ||
"""Tests the computation of the sensitivities from the Aesara computation graph""" | ||
|
||
# ODE system for which to compute gradients | ||
def ode_func(y, t, p): | ||
return np.exp(-t) - p[0] * y[0] | ||
|
||
# Computation of graidients with Aesara | ||
augmented_ode_func = augment_system(ode_func, 1, 1 + 1) | ||
|
||
# This is the new system, ODE + Sensitivities, which will be integrated | ||
def augmented_system(Y, t, p): | ||
dydt, ddt_dydp = augmented_ode_func(Y[:1], t, p, Y[1:]) | ||
derivatives = np.concatenate([dydt, ddt_dydp]) | ||
return derivatives | ||
|
||
# Create real sensitivities | ||
y0 = 0.0 | ||
t = np.arange(0, 12, 0.25).reshape(-1, 1) | ||
a = 0.472 | ||
p = np.array([y0, a]) | ||
|
||
# Derivatives of the analytic solution with respect to y0 and alpha | ||
# Treat y0 like a parameter and solve analytically. Then differentiate. | ||
# I used CAS to get these derivatives | ||
y0_sensitivity = np.exp(-a * t) | ||
a_sensitivity = ( | ||
-(np.exp(t * (a - 1)) - 1 + (a - 1) * (y0 * a - y0 - 1) * t) * np.exp(-a * t) / (a - 1) ** 2 | ||
) | ||
|
||
sensitivity = np.c_[y0_sensitivity, a_sensitivity] | ||
|
||
integrated_solutions = ode.odeint(func=augmented_system, y0=[y0, 1, 0], t=t.ravel(), args=(p,)) | ||
simulated_sensitivity = integrated_solutions[:, 1:] | ||
|
||
np.testing.assert_allclose(sensitivity, simulated_sensitivity, rtol=1e-5) |