`scipy.sparse.linalg._onenormest:onenormest`

source: /scipy/sparse/linalg/_onenormest.py :11

Signature

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

Summary

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

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 array.
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.

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."

Examples

import numpy as np
from scipy.sparse import csc_array
from scipy.sparse.linalg import onenormest
A = csc_array([[1., 0., 0.], [5., 8., 2.], [0., -1., 0.]], dtype=float)
A.toarray()

✓

onenormest(A)
np.linalg.norm(A.toarray(), ord=1)

✗

Aliases

scipy.sparse.linalg.onenormest