lrux.pf

lrux.pf(A: Array, *, method: str = 'householder') → Array

Compute the pfaffian of an array.

Parameters:

• A – An array with shape (…, n, n)

• method –

  The method used to compute the pfaffian. Options include

  "householder":

  Houserholder transformation, internally using jax.lax.fori_loop to balance between running and compiling time;

  "householder_for":

  Houserholder transformation, internally using jitted python for loops to reduce the running time at a cost of much longer compiling time;

  "schur":

  Schur decomposition using jax.scipy.linalg.schur, but only available on CPU and real dtypes.

  The default method is "householder".

Returns:

The pfaffian of A with the same batch dimensions.

Tip

The input A is always be skew-symmetrized.

Tip

This function has jax.custom_jvp defined and is backward compatible for both real and complex dtypes.