Replace deprecated jax context manager and JIT-traced non-array arguments

[hannes-holey]

Hi, thank you for tinygp.

This PR attempts to replace the jax.experimental.enable_x64 context manager which is deprecated in jax>=0.9.0.

While testing this change on current GitHub runners some other JAX-related issues surfaced:

See details

Downloading cpython-3.10.19-linux-x86_64-gnu (download) (28.5MiB)
 Downloaded cpython-3.10.19-linux-x86_64-gnu (download)
Using CPython 3.10.19
Creating virtual environment at: .venv
   Building tinygp @ file:///home/runner/work/tinygp/tinygp
Downloading pygments (1.2MiB)
Downloading scipy (35.9MiB)
Downloading numpy (16.0MiB)
Downloading ml-dtypes (4.8MiB)
Downloading jaxlib (85.8MiB)
Downloading jax (2.6MiB)
      Built tinygp @ file:///home/runner/work/tinygp/tinygp
 Downloaded ml-dtypes
 Downloaded pygments
 Downloaded jax
 Downloaded jaxlib
 Downloaded numpy
 Downloaded scipy
Installed 20 packages in 41ms
============================= test session starts ==============================
platform linux -- Python 3.10.19, pytest-9.0.2, pluggy-1.6.0
rootdir: /home/runner/work/tinygp/tinygp
configfile: pyproject.toml
plugins: xdist-3.8.0, jaxtyping-0.3.6
created: 4/4 workers
4 workers [130 items]

.F...F.................................................................. [ 55%]
.....................................................s....               [100%]
=================================== FAILURES ===================================
_________________________________ test_sample __________________________________
[gw0] linux -- Python 3.10.19 /home/runner/work/tinygp/tinygp/.venv/bin/python
jax.errors.SimplifiedTraceback: For simplicity, JAX has removed its internal frames from the traceback of the following exception. Set JAX_TRACEBACK_FILTERING=off to include these.

The above exception was the direct cause of the following exception:

data = (array([[ 1.44739616, -2.54217712, -1.74711698, -1.02426555,  2.73445279],
       [ 0.68050516,  0.00431724, -0.836095....52507338,  2.89057525],
       [ 0.59347335, -2.85087174, -1.22763876,  0.39915777, -0.62558987]]), 50.35871298268382)

    def test_sample(data):
        X, _ = data
    
        with jax_enable_x64():
            gp = GaussianProcess(
                kernels.Matern32(1.5), X, diag=0.01, mean=lambda x: jnp.sum(x)
            )
>           y = gp.sample(jax.random.PRNGKey(543))

tests/test_gp.py:31: 
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 

self = GaussianProcess(
  num_data=50,
  dtype=dtype('float64'),
  kernel=Matern32(scale=1.5, distance=L1Distance()),
  X=f64...r(
    X=f64[50,5](numpy),
    variance_value=f64[50],
    covariance_value=f64[50,50],
    scale_tril=f64[50,50]
  )
)
key = Array([  0, 543], dtype=uint32), shape = None

    def sample(
        self,
        key: jax.random.KeyArray,
        shape: Sequence[int] | None = None,
    ) -> JAXArray:
        """Generate samples from the prior process
    
        Args:
            key: A ``jax`` random number key array. shape (tuple, optional): The
            number and shape of samples to
                generate.
    
        Returns:
            The sampled realizations from the process with shape ``(N_data,) +
            shape`` where ``N_data`` is the zeroth dimension of the ``X``
            coordinates provided when instantiating this process.
        """
>       return self._sample(key, shape)
E       TypeError: Error interpreting argument to <function GaussianProcess._sample at 0x7f8a7a0f1750> as an abstract array. The problematic value is of type <class 'equinox._module._flatten._Missing'> and was passed to the function at path self.mean_function.value.
E       This typically means that a jit-wrapped function was called with a non-array argument, and this argument was not marked as static using the static_argnums or static_argnames parameters of jax.jit.

src/tinygp/gp.py:291: TypeError
__________________________________ test_means __________________________________
[gw0] linux -- Python 3.10.19 /home/runner/work/tinygp/tinygp/.venv/bin/python
jax.errors.SimplifiedTraceback: For simplicity, JAX has removed its internal frames from the traceback of the following exception. Set JAX_TRACEBACK_FILTERING=off to include these.

The above exception was the direct cause of the following exception:

data = (array([[ 1.44739616, -2.54217712, -1.74711698, -1.02426555,  2.73445279],
       [ 0.68050516,  0.00431724, -0.836095....52507338,  2.89057525],
       [ 0.59347335, -2.85087174, -1.22763876,  0.39915777, -0.62558987]]), 50.35871298268382)

    def test_means(data):
        X, y = data
    
        gp1 = GaussianProcess(kernels.Matern32(1.5), X, diag=0.01, mean=lambda x: 0.0)
        gp2 = GaussianProcess(kernels.Matern32(1.5), X, diag=0.01, mean=0.0)
        gp3 = GaussianProcess(kernels.Matern32(1.5), X, diag=0.01)
    
        assert_allclose(gp1.mean, gp2.mean)
        assert_allclose(gp1.mean, gp3.mean)
>       assert_allclose(gp1.log_probability(y), gp2.log_probability(y))

tests/test_gp.py:52: 
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 

self = GaussianProcess(
  num_data=50,
  dtype=dtype('float32'),
  kernel=Matern32(scale=1.5, distance=L1Distance()),
  X=f64...r(
    X=f64[50,5](numpy),
    variance_value=f32[50],
    covariance_value=f32[50,50],
    scale_tril=f32[50,50]
  )
)
y = 50.35871298268382

    def log_probability(self, y: JAXArray) -> JAXArray:
        """Compute the log probability of this multivariate normal
    
        Args:
            y (JAXArray): The observed data. This should have the shape
                ``(N_data,)``, where ``N_data`` was the zeroth axis of the ``X``
                data provided when instantiating this object.
    
        Returns:
            The marginal log probability of this multivariate normal model,
            evaluated at ``y``.
        """
>       return self._compute_log_prob(self._get_alpha(y))
E       TypeError: Error interpreting argument to <function GaussianProcess._get_alpha at 0x7f8a7a0f1ab0> as an abstract array. The problematic value is of type <class 'equinox._module._flatten._Missing'> and was passed to the function at path self.mean_function.value.
E       This typically means that a jit-wrapped function was called with a non-array argument, and this argument was not marked as static using the static_argnums or static_argnames parameters of jax.jit.

src/tinygp/gp.py:139: TypeError
=========================== short test summary info ============================
FAILED tests/test_gp.py::test_sample - TypeError: Error interpreting argument to <function GaussianProcess._sample at 0x7f8a7a0f1750> as an abstract array. The problematic value is of type <class 'equinox._module._flatten._Missing'> and was passed to the function at path self.mean_function.value.
This typically means that a jit-wrapped function was called with a non-array argument, and this argument was not marked as static using the static_argnums or static_argnames parameters of jax.jit.
FAILED tests/test_gp.py::test_means - TypeError: Error interpreting argument to <function GaussianProcess._get_alpha at 0x7f8a7a0f1ab0> as an abstract array. The problematic value is of type <class 'equinox._module._flatten._Missing'> and was passed to the function at path self.mean_function.value.
This typically means that a jit-wrapped function was called with a non-array argument, and this argument was not marked as static using the static_argnums or static_argnames parameters of jax.jit.
============= 2 failed, 127 passed, 2 skipped in 62.09s (0:01:02) ==============

As far as I can tell, the problem was the None attribute of the Mean class when initiated with a callable. This PR should fix this by setting its value attribute to a valid (dummy) JAX array.