pymor.algorithms.randrangefinder

Module Contents

Functions

adaptive_rrf	Adaptive randomized range approximation of A.
rrf	Randomized range approximation of A.

pymor.algorithms.randrangefinder.adaptive_rrf(A, source_product=None, range_product=None, tol=0.0001, failure_tolerance=1e-15, num_testvecs=20, lambda_min=None, iscomplex=False)

Adaptive randomized range approximation of A.

This is an implementation of Algorithm 1 in [BS18].

Given the Operator A, the return value of this method is the VectorArray B with the property

\[\Vert A - P_{span(B)} A \Vert \leq tol\]

with a failure probability smaller than failure_tolerance, where the norm denotes the operator norm. The inner product of the range of A is given by range_product and the inner product of the source of A is given by source_product.

Parameters

A

The Operator A.

source_product

Inner product Operator of the source of A.

range_product

Inner product Operator of the range of A.

tol

Error tolerance for the algorithm.

failure_tolerance

Maximum failure probability.

num_testvecs

Number of test vectors.

lambda_min

The smallest eigenvalue of source_product. If None, the smallest eigenvalue is computed using scipy.

iscomplex

If True, the random vectors are chosen complex.

Returns

B

VectorArray which contains the basis, whose span approximates the range of A.

pymor.algorithms.randrangefinder.rrf(A, source_product=None, range_product=None, q=2, l=8, iscomplex=False)

Randomized range approximation of A.

This is an implementation of Algorithm 4.4 in [HMT11].

Given the Operator A, the return value of this method is the VectorArray Q whose vectors form an approximate orthonomal basis for the range of A.

Parameters

A

The Operator A.

source_product

Inner product Operator of the source of A.

range_product

Inner product Operator of the range of A.

q

The number of power iterations.

l

The block size of the normalized power iterations.

iscomplex

If True, the random vectors are chosen complex.

Returns

Q

VectorArray which contains the basis, whose span approximates the range of A.