onenormest(A, t=2, itmax=5, compute_v=False, compute_w=False)
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."
A linear operator that can be transposed and that can produce matrix products.
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.
Use at most this many iterations.
Request a norm-maximizing linear operator input vector if True.
Request a norm-maximizing linear operator output vector if True.
An underestimate of the 1-norm of the sparse matrix.
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.
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.
>>> 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) 9.0See :
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.sparse.linalg._onenormest.onenormest
Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.
Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)
SVG is more flexible but power hungry; and does not scale well to 50 + nodes.
All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them