gf_cont_struct_get

General function for querying information about cont_struct objects and for applying them to numerical continuation.

# Calling Sequence

    h = gf_cont_struct_get(cont_struct CS, 'init step size')

    t = gf_cont_struct_get(cont_struct CS, 'init test function', vec solution, scalar parameter, vec tangent_sol, scalar tangent_par)

    E = gf_cont_struct_get(cont_struct CS, 'init Moore-Penrose continuation', vec solution, scalar parameter, scalar init_dir)

    E = gf_cont_struct_get(cont_struct CS, 'Moore-Penrose continuation', vec solution, scalar parameter, vec tangent_sol, scalar tangent_par, scalar h)

    t = gf_cont_struct_get(cont_struct CS, 'test function')

    {X, gamma, T_X, T_gamma} = gf_cont_struct_get(cont_struct CS, 'sing_data')

    s = gf_cont_struct_get(cont_struct CS, 'char')

    gf_cont_struct_get(cont_struct CS, 'display')

## Description

General function for querying information about cont_struct objects and for applying them to numerical continuation.

## Command list

- `h = gf_cont_struct_get(cont_struct CS, 'init step size')`

  Return an initial step size for continuation.

- `t = gf_cont_struct_get(cont_struct CS, 'init test function', vec solution, scalar parameter, vec tangent_sol, scalar tangent_par)`

  Initialise the border of the bordered system that serves for calculating the test function for bifurcations. Return the value of the test function for the point given by `solution` and `parameter` and the tangent given by `tangent_sol` and `tangent_par`.

- `E = gf_cont_struct_get(cont_struct CS, 'init Moore-Penrose continuation', vec solution, scalar parameter, scalar init_dir)`

  Initialise the Moore-Penrose continuation: Return a unit tangent to the solution curve at the point given by `solution` and `parameter`, and an initial step size for the continuation. Orientation of the computed tangent with respect to the parameter is determined by the sign of `init_dir`.

- `E = gf_cont_struct_get(cont_struct CS, 'Moore-Penrose continuation', vec solution, scalar parameter, vec tangent_sol, scalar tangent_par, scalar h)`

  Compute one step of the Moore-Penrose continuation: Take the point given by `solution` and `parameter`, the tangent given by `tangent_sol` and `tangent_par`, and the step size `h`. Return a new point on the solution curve, the corresponding tangent and a step size for the next step. If the returned step size equals zero, the continuation has failed. Optionally, return the type of any detected bifurcation point. NOTE: The new point need not to be saved in the model in the end!

- `t = gf_cont_struct_get(cont_struct CS, 'test function')`

  Return the last value of the test function and eventaully the whole calculated graph when passing between subdomains of different smooth pieces.

- `{X, gamma, T_X, T_gamma} = gf_cont_struct_get(cont_struct CS, 'sing_data')`

  Return a singular point (`X`, `gamma`) encountered in the last continuation step (if any) and a couple of arrays (`T_X`, `T_gamma`) of tangents to all located solution branches, which emanate from there.

- `s = gf_cont_struct_get(cont_struct CS, 'char')`

  Output a (unique) string representation of the cont_struct. This can be used for performing comparisons between two different cont_struct objects. This function is to be completed.

- `gf_cont_struct_get(cont_struct CS, 'display')`

  Display a short summary for a cont_struct object.

## See Also

- getfem types

## Authors

Y. Collette