matfree.hutchinson

matfree.hutchinson

Hutchinson-style estimation.

matfree.hutchinson.hutchinson(integrand_fun, /, sample_fun)

Construct Hutchinson's estimator.

Parameters:

• integrand_fun –

  The integrand function. For example, the return-value of integrand_trace. But any other integrand works, too.

• sample_fun –

  The sample function. Usually, either sampler_normal or sampler_rademacher.

Returns:

• integrand_fun –

  A function that maps a random key to an estimate. This function can be jitted, vmapped, or looped over as the user desires.

matfree.hutchinson.integrand_diagonal(matvec)

Construct the integrand for estimating the diagonal.

When plugged into the Monte-Carlo estimator, the result will be an Array or PyTree of Arrays with the same tree-structure as matvec(*args_like) where *args_like is an argument of the sampler.

matfree.hutchinson.integrand_frobeniusnorm_squared(matvec)

Construct the integrand for estimating the squared Frobenius norm.

matfree.hutchinson.integrand_trace(matvec)

Construct the integrand for estimating the trace.

matfree.hutchinson.integrand_trace_and_diagonal(matvec)

Construct the integrand for estimating the trace and diagonal jointly.

matfree.hutchinson.integrand_wrap_moments(integrand_fun, /, moments)

Wrap an integrand into another integrand that computes moments.

Parameters:

• integrand_fun –

  Any integrand function compatible with Hutchinson-style estimation.

• moments –

  Any Pytree (tuples, lists, dictionaries) whose leafs that are valid inputs to lambda m: x**m for an array x, usually, with data-type float (but that depends on the wrapped integrand). For example, moments=4, moments=(1,2), or moments={"a": 1, "b": 2}.

Returns:

• integrand_fun –

  An integrand function compatible with Hutchinson-style estimation whose output has a PyTree-structure that mirrors the structure of the moments argument.

matfree.hutchinson.sampler_normal(*args_like, num)

Construct a function that samples from a standard-normal distribution.

matfree.hutchinson.sampler_rademacher(*args_like, num)

Construct a function that samples from a Rademacher distribution.