General function for querying information about cont_struct objects and for applying them to numerical continuation.
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')
General function for querying information about cont_struct objects and for applying them to numerical continuation.
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.
Y. Collette