Compute the (Moore-Penrose) pseudo-inverse of a matrix.
JAX implementation of numpy.linalg.pinv().
a (ArrayLike) – array of shape (..., M, N) containing matrices to pseudo-invert.
rtol (ArrayLike | None) – float or array_like of shape a.shape[:-2]. Specifies the cutoff for small singular values.of shape (...,). Cutoff for small singular values; singular values smaller rtol * largest_singular_value are treated as zero. The default is determined based on the floating point precision of the dtype.
hermitian (bool) – if True, then the input is assumed to be Hermitian, and a more efficient algorithm is used (default: False)
rcond (ArrayLike | DeprecatedArg | None) – deprecated alias of the rtol argument. Will result in a DeprecationWarning if used.
An array of shape (..., N, M) containing the pseudo-inverse of a.
Notes
jax.numpy.linalg.pinv() differs from numpy.linalg.pinv() in the default value of rcond`: in NumPy, the default is 1e-15. In JAX, the default is 10. * max(num_rows, num_cols) * jnp.finfo(dtype).eps.
Examples
>>> a = jnp.array([[1, 2],
... [3, 4],
... [5, 6]])
>>> a_pinv = jnp.linalg.pinv(a)
>>> a_pinv
Array([[-1.333332 , -0.33333257, 0.6666657 ],
[ 1.0833322 , 0.33333272, -0.41666582]], dtype=float32)
The pseudo-inverse operates as a multiplicative inverse so long as the output is not rank-deficient:
>>> jnp.allclose(a_pinv @ a, jnp.eye(2), atol=1E-4) Array(True, dtype=bool)
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