REQUIRE "ivpsystem.a4l";
REQUIRE "atoms.a4l";

IMPORT "johnpye/extpy/extpy";
IMPORT "johnpye/solve";

(* ASCEND model based on the 'idadenx.c' example problem that accomanpanies IDA *)
MODEL idadenx;
	y1, y2, y3 IS_A factor;
	dy1_dt IS_A factor;
	dy2_dt IS_A factor;

	eq1: dy1_dt = -0.04 * y1 + 1e4 * y2*y3;
	eq2: dy2_dt = +0.04 * y1 - 1e4 * y2*y3 - 3e7*y2^2;
	eq3: 0 = y1 + y2 + y3 - 1;
	
	t IS_A time;
METHODS

METHOD values; (* initial values *)
	y1 := 1;
	y2 := 0;
	y3 := 0;
	t := 0 {s};
END values;

METHOD specify;
	FIX y1, y2;
END specify;

METHOD ode_init;
	FREE y1, y2;
	t.ode_type := -1; t := 0 {s};
	dy1_dt.ode_id := 1; dy1_dt.ode_type := 2;
	y1.ode_id := 1; y1.ode_type := 1;

	dy2_dt.ode_id := 2; dy2_dt.ode_type := 2;
	y2.ode_id := 2; y2.ode_type := 1;

	y3.ode_id := 3;

	t.obs_id := 1;
	y1.obs_id := 2;
	y2.obs_id := 3;
	y3.obs_id := 4;
	dy1_dt.obs_id := 5;
	dy2_dt.obs_id := 6;

	y1.ode_atol := 1e-8;
	y2.ode_atol := 1e-14;
	y3.ode_atol := 1e-6;
END ode_init;
	
METHOD on_load;
	RUN reset; RUN values;
	EXTERNAL solve(SELF);
	RUN ode_init;
END on_load;

END idadenx;