scikits-odes-core

class scikits_odes_core.DaeBase(Rfn, **options)

The interface which DAE solvers must implement.

Parameters:

• Rfn (function) – residual function

• options (mapping) – Additional options for initialization, solver dependent

init_step(t0, y0, yp0, y_ic0_retn=None, yp_ic0_retn=None)

Initializes the solver and allocates memory.

Parameters:

• t0 (number) – initial time

• y0 (list/array) – initial condition for y

• yp0 (list/array) – initial condition for yp

• y_ic0 (numpy array) – (optional) returns the calculated consistent initial condition for y

• yp_ic0 (numpy array) – (optional) returns the calculated consistent initial condition for y derivated.

Returns:

• old_api is False (namedtuple) – namedtuple with the following attributes

  Field	Meaning
  flag	An integer flag (StatusEnumXXX)
  values	Named tuple with entries t and y and ydot. y will correspond to y_retn value and ydot to yp_retn!
  errors	Named tuple with entries t and y and ydot
  roots	Named tuple with entries t and y and ydot
  tstop	Named tuple with entries t and y and ydot
  message	String with message in case of an error

• old_api is True (tuple) – tuple with the following elements in order

  Field	Meaning
  flag	status of the computation (successful or error occurred)
  t_out	time, where the solver stopped (when no error occurred, t_out == t)

set_options(**options)

Set specific options for the solver.

Calling set_options a second time, normally resets the solver.

solve(tspan, y0, yp0)

Runs the solver.

Parameters:

• tspan (list/array) – A list of times at which the computed value will be returned. Must contain the start time as first entry.

• y0 (list/array) – List of initial values

• yp0 (list/array) – List of initial values of derivatives

Returns:

• old_api is False (namedtuple) – namedtuple with the following attributes

  Field	Meaning
  flag	An integer flag (StatusEnumXXX)
  values	Named tuple with entries array t and array y and array ydot. y will correspond to y_retn value and ydot to yp_retn!
  errors	Named tuple with entries t and y and ydot of error
  roots	Named tuple with entries array t and array y and array ydot
  tstop	Named tuple with entries array t and array y and array ydot
  message	String with message in case of an error

• old_api is True (tuple) – tuple with the following elements in order

  Field	Meaning
  flag	indicating return status of the solver
  t	numpy array of times at which the computations were successful
  y	numpy array of values corresponding to times t (values of y[i, :] ~ t[i])
  yp	numpy array of derivatives corresponding to times t (values of yp[i, :] ~ t[i])
  t_err	float or None - if recoverable error occurred (for example reached maximum number of allowed iterations), this is the time at which it happened
  y_err	numpy array of values corresponding to time t_err
  yp_err	numpy array of derivatives corresponding to time t_err

step(t, y_retn=None, yp_retn=None)

Method for calling successive next step of the IDA solver to allow more precise control over the IDA solver. The ‘init_step’ method has to be called before the ‘step’ method.

A step is done towards time t, and output at t returned. This time can be higher or lower than the previous time. If option ‘one_step_compute’==True, and the solver supports it, only one internal solver step is done in the direction of t starting at the current step.

If old_api=True, the old behavior is used: if t>0.0 then integration is performed until this time and results at this time are returned in y_retn; else if if t<0.0 only one internal step is performed towards time abs(t) and results after this one time step are returned.

Parameters:

• t (number)

• y_retn (numpy array (ndim = 1) or None.) – (Needs to be preallocated) If not None, will be filled with y at time t. If None y_retn is not used.

• yp_retn (numpy array (ndim = 1) or None.) – (Needs to be preallocated) If not None, will be filled with derivatives of y at time t. If None yp_retn is not used.

Returns:

• old_api is False (namedtuple) – namedtuple with the following attributes

  Field	Meaning
  flag	An integer flag (StatusEnumXXX)
  values	Named tuple with entries t and y and ydot. y will correspond to y_retn value and ydot to yp_retn!
  errors	Named tuple with entries t and y and ydot
  roots	Named tuple with entries t and y and ydot
  tstop	Named tuple with entries t and y and ydot
  message	String with message in case of an error

• old_api is True (tuple) – tuple with the following elements in order

  Field	Meaning
  flag	status of the computation (successful or error occurred)
  t_out	time, where the solver stopped (when no error occurred, t_out == t)

class scikits_odes_core.OdeBase(Rfn, **options)

The interface which ODE solvers must implement.

Parameters:

• Rfn (function) – A function which computes the required derivatives. The signature should be func(t, y, y_dot, *args, **kwargs). Note that *args and **kwargs handling are solver dependent.

• options (mapping) – Additional options for initialization, solver dependent

init_step(t0, y0)

Initializes the solver and allocates memory.

Parameters:

• t0 (number) – initial time

• y0 (array) – initial condition for y (can be list or numpy array)

Returns:

• old_api is False (namedtuple) – namedtuple with the following attributes

  Field	Meaning
  flag	An integer flag (StatusEnum)
  values	Named tuple with entries t and y
  errors	Named tuple with entries t and y
  roots	Named tuple with entries t and y
  tstop	Named tuple with entries t and y
  message	String with message in case of an error

• old_api is True (tuple) – tuple with the following elements in order

  Field	Meaning
  flag	boolean status of the computation (successful or error occurred)
  t_out	initial time

set_options(**options)

Set specific options for the solver.

Calling set_options a second time, normally resets the solver.

solve(tspan, y0)

Runs the solver.

Parameters:

• tspan (array (or similar)) – a list of times at which the computed value will be returned. Must contain the start time as first entry.

• y0 (array (or similar)) – a list of initial values

Returns:

• old_api is False (namedtuple) – namedtuple with the following attributes

  Field	Meaning
  flag	An integer flag (StatusEnum)
  values	Named tuple with entries t and y
  errors	Named tuple with entries t and y
  roots	Named tuple with entries t and y
  tstop	Named tuple with entries t and y
  message	String with message in case of an error

• old_api is True (tuple) – tuple with the following elements in order

  Field	Meaning
  flag	indicating return status of the solver
  t	numpy array of times at which the computations were successful
  y	numpy array of values corresponding to times t (values of y[i, :] ~ t[i])
  t_err	float or None - if recoverable error occurred (for example reached maximum number of allowed iterations), this is the time at which it happened
  y_err	numpy array of values corresponding to time t_err

step(t, y_retn=None)

Method for calling successive next step of the ODE solver to allow more precise control over the solver. The ‘init_step’ method has to be called before the ‘step’ method.

A step is done towards time t, and output at t returned. This time can be higher or lower than the previous time. If option ‘one_step_compute’==True, and the solver supports it, only one internal solver step is done in the direction of t starting at the current step.

If old_api=True, the old behavior is used: if t>0.0 then integration is performed until this time and results at this time are returned in y_retn if t<0.0 only one internal step is performed towards time abs(t) and results after this one time step are returned

Parameters:

• t (number)

• y_retn (numpy vector (ndim = 1)) – in which the computed value will be stored (needs to be preallocated). If None y_retn is not used.

Returns:

• old_api is False (namedtuple) – namedtuple with the following attributes

  Field	Meaning
  flag	An integer flag (StatusEnum)
  values	Named tuple with entries t and y
  errors	Named tuple with entries t and y
  roots	Named tuple with entries t and y
  tstop	Named tuple with entries t and y
  message	String with message in case of an error

• old_api is True (tuple) – tuple with the following elements in order

  Field	Meaning
  flag	status of the computation (successful or error occurred)
  t_out	time, where the solver stopped (when no error occurred, t_out == t)