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_fragment_3_1(norm_info, n0, tol, m_max=55, ell=2)

Notes

This is code fragment (3.1) in Al-Mohy and Higham (2011). The discussion of default values for m_max and ell is given between the definitions of equation (3.11) and the definition of equation (3.12).

Parameters

norm_info : LazyOperatorNormInfo

Information about norms of certain linear operators of interest.

n0 : int

Number of columns in the _expm_multiply_* B matrix.

tol : float

Expected to be $2^{-24}$ for single precision or $2^{-53}$ for double precision.

m_max : int

A value related to a bound.

ell : int

The number of columns used in the 1-norm approximation. This is usually taken to be small, maybe between 1 and 5.

Returns

best_m : int

Related to bounds for error control.

best_s : int

Amount of scaling.

A helper function for the _expm_multiply_* functions.

Examples

See :

Local connectivity graph

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


GitHub : /scipy/sparse/linalg/_expm_multiply.py#419
type: <class 'function'>
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