ode_test.py

# Copyright 2020 The JAX Authors.
#
# 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
#
#     https://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.

from functools import partial

from absl.testing import absltest
import numpy as np

import jax
from jax._src import test_util as jtu
import jax.numpy as jnp
from jax.experimental.ode import odeint

import scipy.integrate as osp_integrate

from jax import config
config.parse_flags_with_absl()


class ODETest(jtu.JaxTestCase):

  def check_against_scipy(self, fun, y0, tspace, *args, tol=1e-1):
    y0, tspace = np.array(y0), np.array(tspace)
    np_fun = partial(fun, np)
    scipy_result = jnp.asarray(osp_integrate.odeint(np_fun, y0, tspace, args))

    y0, tspace = jnp.array(y0), jnp.array(tspace)
    jax_fun = partial(fun, jnp)
    jax_result = odeint(jax_fun, y0, tspace, *args)

    self.assertAllClose(jax_result, scipy_result, check_dtypes=False, atol=tol, rtol=tol)

  @jtu.skip_on_devices("tpu")
  def test_pend_grads(self):
    def pend(_np, y, _, m, g):
      theta, omega = y
      return [omega, -m * omega - g * _np.sin(theta)]

    y0 = [np.pi - 0.1, 0.0]
    ts = np.linspace(0., 1., 11)
    args = (0.25, 9.8)
    tol = 1e-1 if jtu.num_float_bits(np.float64) == 32 else 1e-3

    self.check_against_scipy(pend, y0, ts, *args, tol=tol)

    integrate = partial(odeint, partial(pend, jnp))
    jtu.check_grads(integrate, (y0, ts, *args), modes=["rev"], order=2,
                    atol=tol, rtol=tol)

  @jtu.skip_on_devices("tpu", "gpu")
  def test_pytree_state(self):
    """Test calling odeint with y(t) values that are pytrees."""
    def dynamics(y, _t):
      return jax.tree.map(jnp.negative, y)

    y0 = (np.array(-0.1), np.array([[[0.1]]]))
    ts = np.linspace(0., 1., 11)
    tol = 1e-1 if jtu.num_float_bits(np.float64) == 32 else 1e-3

    integrate = partial(odeint, dynamics)
    jtu.check_grads(integrate, (y0, ts), modes=["rev"], order=2,
                    atol=tol, rtol=tol)

  @jtu.skip_on_devices("tpu")
  def test_weird_time_pendulum_grads(self):
    """Test that gradients are correct when the dynamics depend on t."""
    def dynamics(_np, y, t):
      return _np.array([y[1] * -t, -1 * y[1] - 9.8 * _np.sin(y[0])])

    y0 = [np.pi - 0.1, 0.0]
    ts = np.linspace(0., 1., 11)
    tol = 1e-1 if jtu.num_float_bits(np.float64) == 32 else 1e-3

    self.check_against_scipy(dynamics, y0, ts, tol=tol)

    integrate = partial(odeint, partial(dynamics, jnp))
    jtu.check_grads(integrate, (y0, ts), modes=["rev"], order=2,
                    rtol=tol, atol=tol)

  @jtu.skip_on_devices("tpu", "gpu")
  def test_decay(self):
    def decay(_np, y, t, arg1, arg2):
        return -_np.sqrt(t) - y + arg1 - _np.mean((y + arg2)**2)


    rng = self.rng()
    args = (rng.randn(3), rng.randn(3))
    y0 = rng.randn(3)
    ts = np.linspace(0.1, 0.2, 4)
    tol = 1e-1 if jtu.num_float_bits(np.float64) == 32 else 1e-3

    self.check_against_scipy(decay, y0, ts, *args, tol=tol)

    integrate = partial(odeint, partial(decay, jnp))
    jtu.check_grads(integrate, (y0, ts, *args), modes=["rev"], order=2,
                    rtol=tol, atol=tol)

  @jtu.skip_on_devices("tpu", "gpu")
  def test_swoop(self):
    def swoop(_np, y, t, arg1, arg2):
      return _np.array(y - _np.sin(t) - _np.cos(t) * arg1 + arg2)

    ts = np.array([0.1, 0.2])
    tol = 1e-1 if jtu.num_float_bits(np.float64) == 32 else 1e-3
    y0 = np.linspace(0.1, 0.9, 10)
    args = (0.1, 0.2)

    self.check_against_scipy(swoop, y0, ts, *args, tol=tol)

    integrate = partial(odeint, partial(swoop, jnp))
    jtu.check_grads(integrate, (y0, ts, *args), modes=["rev"], order=2,
                    rtol=tol, atol=tol)

  @jtu.skip_on_devices("tpu", "gpu")
  def test_swoop_bigger(self):
    def swoop(_np, y, t, arg1, arg2):
      return _np.array(y - _np.sin(t) - _np.cos(t) * arg1 + arg2)

    ts = np.array([0.1, 0.2])
    tol = 1e-1 if jtu.num_float_bits(np.float64) == 32 else 1e-3
    big_y0 = np.linspace(1.1, 10.9, 10)
    args = (0.1, 0.3)

    self.check_against_scipy(swoop, big_y0, ts, *args, tol=tol)

    integrate = partial(odeint, partial(swoop, jnp))
    jtu.check_grads(integrate, (big_y0, ts, *args), modes=["rev"], order=2,
                    rtol=tol, atol=tol)

  @jtu.skip_on_devices("tpu", "gpu")
  def test_odeint_vmap_grad(self):
    # https://github.com/google/jax/issues/2531

    def dx_dt(x, *args):
      return 0.1 * x

    def f(x, y):
      y0 = jnp.array([x, y])
      t = jnp.array([0., 5.])
      y = odeint(dx_dt, y0, t)
      return y[-1].sum()

    def g(x):
      # Two initial values for the ODE
      y0_arr = jnp.array([[x, 0.1],
                         [x, 0.2]])

      # Run ODE twice
      t = jnp.array([0., 5.])
      y = jax.vmap(lambda y0: odeint(dx_dt, y0, t))(y0_arr)
      return y[:,-1].sum()

    ans = jax.grad(g)(2.)  # don't crash
    expected = jax.grad(f, 0)(2., 0.1) + jax.grad(f, 0)(2., 0.2)

    atol = {jnp.float32: 1e-5, jnp.float64: 5e-15}
    rtol = {jnp.float32: 1e-5, jnp.float64: 2e-15}
    self.assertAllClose(ans, expected, check_dtypes=False, atol=atol, rtol=rtol)

  @jtu.skip_on_devices("tpu", "gpu")
  def test_disable_jit_odeint_with_vmap(self):
    # https://github.com/google/jax/issues/2598
    with jax.disable_jit():
      t = jnp.array([0.0, 1.0])
      x0_eval = jnp.zeros((5, 2))
      f = lambda x0: odeint(lambda x, _t: x, x0, t)
      jax.vmap(f)(x0_eval)  # doesn't crash

  @jtu.skip_on_devices("tpu", "gpu")
  def test_grad_closure(self):
    # simplification of https://github.com/google/jax/issues/2718
    def experiment(x):
      def model(y, t):
        return -x * y
      history = odeint(model, 1., np.arange(0, 10, 0.1))
      return history[-1]
    jtu.check_grads(experiment, (0.01,), modes=["rev"], order=1)

  @jtu.skip_on_devices("tpu", "gpu")
  def test_grad_closure_with_vmap(self):
    # https://github.com/google/jax/issues/2718
    @jax.jit
    def experiment(x):
      def model(y, t):
        return -x * y
      history = odeint(model, 1., np.arange(0, 10, 0.1))
      return history[-1]

    gradfun = jax.value_and_grad(experiment)
    t = np.arange(0., 1., 0.01)
    h, g = jax.vmap(gradfun)(t)  # doesn't crash
    ans = h[11], g[11]

    expected_h = experiment(t[11])
    expected_g = (experiment(t[11] + 1e-5) - expected_h) / 1e-5
    expected = expected_h, expected_g

    self.assertAllClose(ans, expected, check_dtypes=False, atol=1e-2, rtol=1e-2)

  @jtu.skip_on_devices("tpu", "gpu")
  def test_forward_mode_error(self):
    # https://github.com/google/jax/issues/3558

    def f(k):
      return odeint(lambda x, t: k*x, 1.,  jnp.linspace(0, 1., 50)).sum()

    with self.assertRaisesRegex(TypeError, "can't apply forward-mode.*"):
      jax.jacfwd(f)(3.)

  @jtu.skip_on_devices("tpu", "gpu")
  def test_closure_nondiff(self):
    # https://github.com/google/jax/issues/3584

    def dz_dt(z, t):
      return jnp.stack([z[0], z[1]])

    def f(z):
      y = odeint(dz_dt, z, jnp.arange(10.))
      return jnp.sum(y)

    jax.grad(f)(jnp.ones(2))  # doesn't crash

  @jtu.skip_on_devices("tpu", "gpu")
  def test_complex_odeint(self):
    # https://github.com/google/jax/issues/3986
    # https://github.com/google/jax/issues/8757

    def dy_dt(y, t, alpha):
      return alpha * y * jnp.exp(-t).astype(y.dtype)

    def f(y0, ts, alpha):
      return odeint(dy_dt, y0, ts, alpha).real

    alpha = 3 + 4j
    y0 = 1 + 2j
    ts = jnp.linspace(0., 1., 11)
    tol = 1e-1 if jtu.num_float_bits(np.float64) == 32 else 1e-3

    # During the backward pass, this ravels all parameters into a single array
    # such that dtype promotion is unavoidable.
    with jax.numpy_dtype_promotion('standard'):
      jtu.check_grads(f, (y0, ts, alpha), modes=["rev"], order=2, atol=tol, rtol=tol)

  @jtu.skip_on_devices("tpu", "gpu")
  def test_hmax(self):
    """Test max step size control."""

    def rhs(y, t):
      return jnp.piecewise(
        t,
        [t <= 2., (t >= 5.) & (t <= 7.)],
        [lambda s: jnp.array(1.), lambda s: jnp.array(-1.), lambda s: jnp.array(0.)]
      )
    ys = odeint(func=rhs, y0=jnp.array(0.), t=jnp.array([0., 5., 10.]), hmax=1.)

    self.assertTrue(jnp.abs(ys[1] - 2.) < 1e-4)
    self.assertTrue(jnp.abs(ys[2]) < 1e-4)


if __name__ == '__main__':
  absltest.main(testLoader=jtu.JaxTestLoader())