jax.scipy.linalg.funm#

jax.scipy.linalg.funm(A, func, disp=True)[source]#

Evaluate a matrix-valued function

JAX implementation of `scipy.linalg.funm()`.

Parameters:
• A (jax.typing.ArrayLike) â€“ array of shape `(N, N)` for which the function is to be computed.

• func (Callable[[Array], Array]) â€“ Callable object that takes a scalar argument and returns a scalar result. Represents the function to be evaluated over the eigenvalues of A.

• disp (bool) â€“ If true (default), error information is not returned. Unlike scipyâ€™s version JAX does not attempt to display information at runtime.

• compute_expm â€“ (N, N) array_like or None, optional. If provided, the matrix exponential of A. This is used for improving efficiency when func is the exponential function. If not provided, it is computed internally. Defaults to None.

Returns:

Array of same shape as `A`, containing the result of `func` evaluated on the eigenvalues of `A`.

Return type:

Notes

The returned dtype of JAXâ€™s implementation may differ from that of scipy; specifically, in cases where all imaginary parts of the array values are close to zero, the SciPy function may return a real-valued array, whereas the JAX implementation will return a complex-valued array.

Example

Applying an arbitrary matrix function:

```>>> A = jnp.array([[1., 2.], [3., 4.]])
>>> def func(x):
...   return jnp.sin(x) + 2 * jnp.cos(x)
>>> jax.scipy.linalg.funm(A, func)
Array([[ 1.2452652 +0.j, -0.3701772 +0.j],
[-0.55526584+0.j,  0.6899995 +0.j]], dtype=complex64)
```

Comparing two ways of computing the matrix exponent:

```>>> expA_1 = jax.scipy.linalg.funm(A, jnp.exp)
>>> expA_2 = jax.scipy.linalg.expm(A)
>>> jnp.allclose(expA_1, expA_2, rtol=1E-4)
Array(True, dtype=bool)
```