module Quadrature:sig..end
Integration of pure quadrature equations.
Adds a vector $y_Q$ of $N_Q$ quadrature variables defined by $\frac{\mathrm{d} y_Q}{\mathrm{d}t} = f_Q(t, y, \dot{y}, p)$. These are treated more efficiently since they are excluded from the nonlinear solution stage.
type'dquadrhsfn =float -> 'd -> 'd -> 'd -> unit
Functions defining quadrature variables. They are passed four arguments:
t, the value of the independent variable, i.e., the simulation time,y, the vector of dependent-variable values, i.e., $y(t)$,y', the vector of dependent-variable derivatives,
i.e., $\dot{y}(t)$ and,yq', a vector for storing the computed value of
$\dot{y}_Q = f_Q(t, y, \dot{y}, p)$.Within the function, raising a Sundials.RecoverableFailure exception
indicates a recoverable error. Any other exception is treated as an
unrecoverable error.
val init : ('d, 'k) Ida.session ->
'd quadrhsfn -> ('d, 'k) Nvector.t -> unitActivates the integration of quadrature equations. The vector gives the initial value of $y_Q$.
val reinit : ('d, 'k) Ida.session -> ('d, 'k) Nvector.t -> unitReinitializes the integration of quadrature equations. The vector gives a new value for $y_Q$.
val get : ('d, 'k) Ida.session -> ('d, 'k) Nvector.t -> floatReturns the quadrature solutions and time reached after a successful
solver step. The given vector is filled with values calculated during
either Ida.solve_normal or Ida.solve_one_step and the
value of the independent variable is returned.
val get_dky : ('d, 'k) Ida.session -> ('d, 'k) Nvector.t -> float -> int -> unitReturns the interpolated solution or derivatives of quadrature variables.
get_dky s dkyq t k computes the kth derivative at time t, i.e.,
$\frac{d^\mathtt{k}y_Q(\mathtt{t})}{\mathit{dt}^\mathtt{k}}$,
and stores it in dkyq. The arguments must satisfy $t_n - h_u \leq
\mathtt{t} \leq t_n$—where $t_n$ denotes Ida.get_current_time
and $h_u$ denotes Ida.get_last_step,— and
$0 \leq \mathtt{k} \leq q_u$—where
$q_u$ denotes Ida.get_last_order.
This function may only be called after a successful return from either
Ida.solve_normal or Ida.solve_one_step.
BadT t is not in the interval $[t_n - h_u, t_n]$.BadK k is not in the range 0, 1, ..., $q_u$.type ('d, 'k) tolerance =
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NoStepSizeControl |
(* | Do not use quadrature variables for step-size control (default). | *) |
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SStolerances of |
(* |
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SVtolerances of |
(* |
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Tolerances for calculating quadrature variables.
val set_tolerances : ('d, 'k) Ida.session -> ('d, 'k) tolerance -> unitSpecify how to use quadrature variables in step size control.
val get_num_rhs_evals : ('d, 'k) Ida.session -> intReturns the number of calls to the quadrature function.
val get_num_err_test_fails : ('d, 'k) Ida.session -> intReturns the number of local error test failures that have occurred due to quadrature variables.
val get_err_weights : ('d, 'k) Ida.session -> ('d, 'k) Nvector.t -> unitReturns the quadrature error weights at the current time.
val get_stats : ('d, 'k) Ida.session -> int * intReturns quadrature-related statistics. These are the
number of calls to the quadrature function (nfqevals) and the number
of error test failures due to quadrature variables (nqetfails).
nfqevals, nqetfails)exception QuadNotInitialized
Quadrature integration was not initialized.
exception QuadRhsFuncFailure
The quadrature function failed in an unrecoverable manner.
exception FirstQuadRhsFuncFailure
The quadrature function failed at the first call.
exception RepeatedQuadRhsFuncFailure
Convergence test failures occurred too many times due to repeated recoverable errors in the quadrature function. Also raised if the quadrature function had repeated recoverable errors during the estimation of an initial step size (if quadrature variables are included in error tests).