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onenormest(A, t=2, itmax=5, compute_v=False, compute_w=False)

Notes

This is algorithm 2.4 of [1].

In [2] it is described as follows. "This algorithm typically requires the evaluation of about 4t matrix-vector products and almost invariably produces a norm estimate (which is, in fact, a lower bound on the norm) correct to within a factor 3."

versionadded

Parameters

A : ndarray or other linear operator

A linear operator that can be transposed and that can produce matrix products.

t : int, optional

A positive parameter controlling the tradeoff between accuracy versus time and memory usage. Larger values take longer and use more memory but give more accurate output.

itmax : int, optional

Use at most this many iterations.

compute_v : bool, optional

Request a norm-maximizing linear operator input vector if True.

compute_w : bool, optional

Request a norm-maximizing linear operator output vector if True.

Returns

est : float

An underestimate of the 1-norm of the sparse matrix.

v : ndarray, optional

The vector such that ||Av||_1 == est*||v||_1. It can be thought of as an input to the linear operator that gives an output with particularly large norm.

w : ndarray, optional

The vector Av which has relatively large 1-norm. It can be thought of as an output of the linear operator that is relatively large in norm compared to the input.

Compute a lower bound of the 1-norm of a sparse matrix.

Examples

>>> from scipy.sparse import csc_matrix
... from scipy.sparse.linalg import onenormest
... A = csc_matrix([[1., 0., 0.], [5., 8., 2.], [0., -1., 0.]], dtype=float)
... A.toarray() array([[ 1., 0., 0.], [ 5., 8., 2.], [ 0., -1., 0.]])
>>> onenormest(A)
9.0
>>> np.linalg.norm(A.toarray(), ord=1)
9.0
See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.sparse.linalg._onenormest.onenormest

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GitHub : /scipy/sparse/linalg/_onenormest.py#11
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