ahkab.trap¶
This file implements the Trapezoidal (TRAP) Differentiation Formula (DF) and a second order prediction formula.
Module reference¶
-
get_df(pv_array, suggested_step, predict=True)[source]¶ Get the coefficients for DF and prediction formula
Parameters:
- pv_array : sequence of sequences
Each element of
pv_arraymust be of the form:(time, x, derivate(x))
In particular, the \(k\) element of pv_array contains the values of:
- \(t_{n-k}\) (the time),
- \(x_{n-k}\),
- \(dx_{n-k}/dt\)
evaluated \(k\) time steps before the current one, labeled \(n+1\).
How many samples are necessary is given by
ahkab.trap.get_required_values().Values that are not needed may be set to
None, as they will be disregarded.- suggested_step : float
- The step that will be used for the current iteration, provided the error will be deemed acceptable.
- predict : bool, optional
- Whether a prediction for \(x_n\) is needed as well or not. Defaults
to
True.
Returns:
- ret : tuple
The return value has the form:
(C1, C0, x_lte_coeff, predict_x, predict_lte_coeff)
The derivative may be written as:
\[d(x(n+1))/dt = C1 x(n+1) + C0\]x_lte_coeff is the coefficient of the Local Truncation Error, predict_x is the predicted value for \(x\) and predict_lte_coeff is the LTE coefficient for the prediction.
Raises: ValueError – if the pv_array is malformed.
-
get_required_values()[source]¶ Get info regarding what values are needed by the DF
Returns:
- tpl : tuple of tuples
A tuple of two tuples.
- The first tuple indicates what past values of the unknown are needed for the DF.
- The second tuple indicates what past values of the unknown are needed for the prediction method.
In particular, each of the sub-tuples is built this way:
(max_order_of_x, max_order_of_dx)
Where both the values are either
int, orNone. Ifmax_order_of_xis set to an integer value \(k\), the DF needs all the \(x_{n-i}\) values of x, for all \(0 \le i \le k\). In the previous text, \(x_{n-i}\) is the value the \(x\) array assumed \(i\) steps before the one we are considering for the derivative.Similar considerations apply to
max_order_of_dx, but regard rather \(dx_n/dt\) instead of \(x_n\).If any of the values is set to
None, it is to be assume that no value is required.
The first array has to be used if no prediction is required, the second are the values needed for prediction.
