Module Odepack


module Odepack: sig .. end
Binding to ODEPACK. This is a collection of solvers for the initial value problem for ordinary differential equation systems.
Author(s): Christophe Troestler (Christophe.Troestler@umons.ac.be)
Version: 0.3

type vec = (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array1.t 
Representation of vectors (parametrized by their layout).
type mat = (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array2.t 
Representation of matrices (parametrized by their layout).
type t 
A mutable value holding the current state of solving the ODE.

type jacobian =
| Auto_full (*Internally generated (difference quotient) full Jacobian*)
| Auto_band of int * int (*Internally generated (difference quotient) band Jacobian. It takes (l,u) where l (resp. u) is the number of lines below (resp. above) the diagonal (excluded).*)
| Full of (float -> vec -> mat -> unit) (*Full df means that a function df is provided to compute the full Jacobian matrix (∂f_i/∂y_j) of the vector field f(t,y). df t y jac must store ∂f_i/∂y_j(t,y) into jac.{i,j}.*)
| Band of int * int * (float -> vec -> int -> mat -> unit) (*Band(l, u, df) means that a function df is provided to compute the banded Jacobian matrix with l (resp. u) diagonals below (resp. above) the main one (not counted). df t y d jac must store ∂f_i/∂y_j(t,y) into jac.{i-j+d, j}. d is the row of jac corresponding to the main diagonal of the Jacobian matrix.*)
Types of Jacobian matrices.
val lsoda : ?rtol:float ->
?rtol_vec:vec ->
?atol:float ->
?atol_vec:vec ->
?jac:jacobian ->
?mxstep:int ->
?copy_y0:bool ->
?debug:bool ->
?debug_switches:bool ->
(float -> vec -> vec -> unit) ->
vec -> float -> float -> t
lsoda f y0 t0 t solves the ODE dy/dt = F(t,y) with initial condition y(t0) = y0. The execution of f t y y' must compute the value of the F(t, y) and store it in y'.
rtol : relative error tolerance parameter. Default 1e-6.
rtol_vec : relative error tolerance vector.
atol : absolute error tolerance parameter. Default 1e-6.
atol_vec : absolute error tolerance vector.

If rtol_vec (resp. atol_vec) is specified, it is used in place of rtol (resp. atol). Specifying only rtol (resp. atol) is equivalent to pass a constant rtol_vec (resp. atol_vec). The solver will control the vector E = (E(i)) of estimated local errors in y, according to an inequality of the form max-norm(E(i)/EWT(i)) <= 1, where EWT(i) = rtol_vec.{i} * abs_float(y.{i}) +. atol_vec.{i}.

jac : is an optional Jabobian matrix. If the problem is expected to be stiff much of the time, you are encouraged to supply jac, for the sake of efficiency. Default: Auto_full.
mxstep : maximum number of (internally defined) steps allowed during one call to the solver. The default value is 500.
copy_y0 : if false, the vector y0 is MODIFIED to contain the value of the solution at time t. Otherwise y0 is unchanged. Default: true.
debug : allows lsoda to print messages. Default true. The messages contain valuable information, it is not recommended to turn them off.
debug_switches : prints a message to stdout on each (automatic) method switch (between nonstiff and stiff). Default: false.
val vec : t -> vec
vec ode returns the current value of the solution vector.
val t : t -> float
t ode returns the current time at which the solution vector was computed.
val advance : t -> float -> unit
advance ode t modifies ode so that an approximation of the value of the solution at times t is computed.
val sol : t -> float -> vec
sol ode t modifies ode so that it holds an approximation of the solution at t and returns this approximation.