# Module Cvode.Dls

module Dls: sig .. end

Direct Linear Solvers operating on dense, banded, and sparse matrices.

include Sundials_LinearSolver.Direct
type 'm jac_fn = (Sundials.RealArray.t Cvode.triple, Sundials.RealArray.t) Cvode.jacobian_arg ->       'm -> unit

Callback functions that compute approximations to a Jacobian matrix. In the call jac arg jm, arg is a Cvode.jacobian_arg with three work vectors and the computed Jacobian must be stored in jm.

The callback should load the (i,j)th entry of jm with $\partial y_i/\partial y_j$, i.e., the partial derivative of the ith equation with respect to the jth variable, evaluated at the values of t and y obtained from arg. Only nonzero elements need be loaded into jm.

Raising Sundials.RecoverableFailure indicates a recoverable error. Any other exception is treated as an unrecoverable error.

Neither the elements of arg nor the matrix jm should be accessed after the function has returned.

type 'm linsys_fn = (Sundials.RealArray.t Cvode.triple, Sundials.RealArray.t) Cvode.jacobian_arg ->       'm -> bool -> float -> bool

Function to compute the linear system matrix $M = I - \gamma J$ or an approximation of it. Offers an alternative to evaluating the Jacobian of the right-hand-side function.

In addition to those shared with the Jacobian function, the arguments of this function are

• m, storage for the computed linear system matrix,
• jok, indicates whether the Jacobian-related data needs to be updated, and
• gamma, the scalar in the formula above.

The function should return true only if the Jacobian data was recomputed.

Raising Sundials.RecoverableFailure indicates a recoverable error. Any other exception is treated as an unrecoverable error.

Neither the Jacobian argument elements nor the matrix m should be accessed after the function has returned.

val solver : ?jac:'m jac_fn ->       ?linsys:'m linsys_fn ->       ('m, Sundials.RealArray.t, [> Nvector_serial.kind ] as 'a, [> Dls ])       Sundials.LinearSolver.t -> 'a Cvode.serial_linear_solver

Create a Cvode-specific linear solver from a Jacobian approximation function and generic direct linear solver.

The Jacobian approximation function is optional for dense and banded solvers (if not given an internal difference quotient approximation is used), but must be provided for other solvers (or Invalid_argument is raised).

The linsys argument allows to override the standard linear system function that calls jac to compute $M$ . This feature is only available in Sundials >= 5.0.0.

#### Solver statistics

val get_work_space : [> Nvector_serial.kind ] Cvode.serial_session -> int * int

Returns the sizes of the real and integer workspaces used by a direct linear solver.

val get_num_jac_evals : [> Nvector_serial.kind ] Cvode.serial_session -> int

Returns the number of calls made by a direct linear solver to the Jacobian approximation function.

val get_num_lin_rhs_evals : [> Nvector_serial.kind ] Cvode.serial_session -> int`

Returns the number of calls to the right-hand side callback due to the finite difference Jacobian approximation.