continuate.arclength

numerical continuation with tangent space

continuate.arclength.concat(x, mu)

Convert \((x, \mu)\) to \(\xi\)

continuate.arclength.continuation(func, x, *args, **kwds)

Generator for continuation of a vector function \(F(x, \mu)\)

Using Newton-Krylov-Hook algorithm in each of continuation steps.

Parameters:

func : (numpy.array, float) -> numpy.array

\(F(x, \mu)\) func(x, mu) must have same dimension of x

x : numpy.array

Initial point of continuation, and satisfies \(F(x, \mu) = 0\)

mu : float

Initial parameter of continuation, and satisfies \(F(x, \mu) = 0\)

delta : float

step length of continuation. To decrease the parameter, you should set negative value.

Yields:

x : numpy.array

\(x\)

mu : float

\(\mu\)

continuate.arclength.default_options = {'tangent_dmu': 1e-07}

default values of options

You can get these values through continuate.get_default_options()

Parameters:

tangentspace_dmu : float

Infinitesimal of parameter \(d\mu\) for calculating \(dx/d\mu\)

continuate.arclength.tangent_vector(func, x, *args, **kwds)

Get tangent vector at \((x, \mu)\)

Parameters:

func : (numpy.array, float) -> numpy.array

\(F(x, \mu)\), func(x, mu) must have same dimension of x

Returns:

dxi : np.array

Tangent vector