test/ipopt/formula.a4c

(*	ASCEND modelling environment

	This program is free software; you can redistribute it and/or modify
	it under the terms of the GNU General Public License as published by
	the Free Software Foundation; either version 2, or (at your option)
	any later version.

	This program is distributed in the hope that it will be useful,
	but WITHOUT ANY WARRANTY; without even the implied warranty of
	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
	GNU General Public License for more details.
	
	You should have received a copy of the GNU General Public License
	along with this program; if not, write to the Free Software
	Foundation, Inc., 59 Temple Place - Suite 330,
	Boston, MA 02111-1307, USA.
*)
IMPORT "ipopt";
REQUIRE "atoms.a4l";
(*
This model is from W A Dollase & W I Newman (1984) 'Statistically most probable
stoichiometric formulae', American Mineralogist (69) 553-556, accessed online at
http://www.minsocam.org/msa/collectors_corner/arc/formula.htm

As of 21 Dec 2010, this file crashes ASCEND if run with IPOPT as the solver.

Model written by Roger Mason, with contributions from John Pye.
*)


(*
A general container for the equations of Dollase & Newman
*)
MODEL formula_base;
	n IS_A integer_constant;   (* number of elements *)
	m IS_A integer_constant;   (* number of constraints *)
	n :== 4;
	m :== 3;

	w[1..n] IS_A factor;       (* weight of oxide, per cation *)
	C[1..m][1..n] IS_A factor; (* constraint coefficients *)
	Cs[1..m] IS_A factor;      (* constraint sums *)
	x[1..n] IS_A  fraction;    (* oxide component concentration *)
	N[1..n] IS_A factor;       (* numbers of moles of each oxide *)
	k IS_A  factor;            (* 'normalisation factor, to be determinied' *)

	y[1..n] IS_A fraction;     (* given weight fraction analyte *)
	s[1..n] IS_A factor;       (* standard deviation in given weight fraction *)

	(* objective function *)
	objective: MINIMIZE SUM[ (y[i] - x[i])^2/s[i]^2 | i IN [1..n]]; (* 1 *)

	(* molecular structure constraints *)
	FOR j IN [1..m] CREATE
		Cs[j] = SUM[ C[j][i]*N[i] | i IN [1..n]]; (* 2 *)
	END FOR;

	FOR i IN [1..n] CREATE
		N[i] = k * x[i]/w[i]; (* 3 *)
	END FOR;

	(* sum of concentrations must equal unity *)
	1 = SUM[ x[i] | i IN [1..n]]; (* 5 *)

END formula_base;

(*
A specific example implementing the above equation: plagioclase feldspar.
*)
MODEL formula REFINES formula_base;

METHODS
METHOD specify;
	FIX C[1..3][1..4];
	FIX Cs[1..4];
	FIX w[1..4];
	FIX y[1..4];
	FIX s[1..4];

	FIX k;
END specify;
METHOD values;
	(* there are 8 total oxygens, *)
	Cs[1] := 8.0;
	C[1][1] := 0.5;
	C[1][2] := 1.0;
	C[1][3] := 1.5;
	C[1][4] := 2.0;

	(* four atoms in tetrahedral sites, and *)
	Cs[2] := 4.0;
	C[2][1] := 0.0;
	C[2][2] := 0.0;
	C[2][3] := 1.0;
	C[2][4] := 1.0;

	(* the sum of Na + Ca is equal to one. *)
	Cs[3] := 1.0;
	C[3][1] := 1.0;
	C[3][2] := 1.0;
	C[3][3] := 0.0;
	C[3][4] := 0.0;

	(* cation weights *)
	w[1] := 30.9895; (* 22.9898 + 15.9994*(1/2) *)
	w[2] := 56.0774;	(* 40.078 + 15.9994 *)
	w[3] := 50.9806;	(* 26.9815 + 15.9994*(3/2) *)
	w[4] := 60.0843;	(* 28.0855 + 15.9994*(2/1) *)

	y[1] := 11.19/100 {};
	y[2] := 1.07/100  {};
	y[3] := 20.35/100 {};
	y[4] := 67.39/100 {};

	k := 2.62925;

	s[1] := 0.05 {};
	s[2] := 0.05 {};
	s[3] := 0.05 {};
	s[4] := 0.05 {};

END values;
METHOD default_self;
	x[1] := 11.29/100 {};
	x[2] := 1.01/100  {};
	x[3] := 20.31/100 {};
	x[4] := 67.30/100 {};
END default_self;

METHOD on_load;
	RUN reset;
	RUN values;
	RUN specify;
END on_load;

METHOD self_test;
END self_test;

END formula;
1	(* ASCEND modelling environment
2
3	This program is free software; you can redistribute it and/or modify
4	it under the terms of the GNU General Public License as published by
5	the Free Software Foundation; either version 2, or (at your option)
6	any later version.
7
8	This program is distributed in the hope that it will be useful,
9	but WITHOUT ANY WARRANTY; without even the implied warranty of
10	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
11	GNU General Public License for more details.
12
13	You should have received a copy of the GNU General Public License
14	along with this program; if not, write to the Free Software
15	Foundation, Inc., 59 Temple Place - Suite 330,
16	Boston, MA 02111-1307, USA.
17	*)
18	IMPORT "ipopt";
19	REQUIRE "atoms.a4l";
20	(*
21	This model is from W A Dollase & W I Newman (1984) 'Statistically most probable
22	stoichiometric formulae', American Mineralogist (69) 553-556, accessed online at
23	http://www.minsocam.org/msa/collectors_corner/arc/formula.htm
24
25	As of 21 Dec 2010, this file crashes ASCEND if run with IPOPT as the solver.
26
27	Model written by Roger Mason, with contributions from John Pye.
28	*)
29
30
31	(*
32	A general container for the equations of Dollase & Newman
33	*)
34	MODEL formula_base;
35	n IS_A integer_constant; (* number of elements *)
36	m IS_A integer_constant; (* number of constraints *)
37	n :== 4;
38	m :== 3;
39
40	w[1..n] IS_A factor; (* weight of oxide, per cation *)
41	C[1..m][1..n] IS_A factor; (* constraint coefficients *)
42	Cs[1..m] IS_A factor; (* constraint sums *)
43	x[1..n] IS_A fraction; (* oxide component concentration *)
44	N[1..n] IS_A factor; (* numbers of moles of each oxide *)
45	k IS_A factor; (* 'normalisation factor, to be determinied' *)
46
47	y[1..n] IS_A fraction; (* given weight fraction analyte *)
48	s[1..n] IS_A factor; (* standard deviation in given weight fraction *)
49
50	(* objective function *)
51	objective: MINIMIZE SUM[ (y[i] - x[i])^2/s[i]^2 \| i IN [1..n]]; (* 1 *)
52
53	(* molecular structure constraints *)
54	FOR j IN [1..m] CREATE
55	Cs[j] = SUM[ C[j][i]N[i] \| i IN [1..n]]; ( 2 *)
56	END FOR;
57
58	FOR i IN [1..n] CREATE
59	N[i] = k * x[i]/w[i]; (* 3 *)
60	END FOR;
61
62	(* sum of concentrations must equal unity *)
63	1 = SUM[ x[i] \| i IN [1..n]]; (* 5 *)
64
65	END formula_base;
66
67	(*
68	A specific example implementing the above equation: plagioclase feldspar.
69	*)
70	MODEL formula REFINES formula_base;
71
72	METHODS
73	METHOD specify;
74	FIX C[1..3][1..4];
75	FIX Cs[1..4];
76	FIX w[1..4];
77	FIX y[1..4];
78	FIX s[1..4];
79
80	FIX k;
81	END specify;
82	METHOD values;
83	(* there are 8 total oxygens, *)
84	Cs[1] := 8.0;
85	C[1][1] := 0.5;
86	C[1][2] := 1.0;
87	C[1][3] := 1.5;
88	C[1][4] := 2.0;
89
90	(* four atoms in tetrahedral sites, and *)
91	Cs[2] := 4.0;
92	C[2][1] := 0.0;
93	C[2][2] := 0.0;
94	C[2][3] := 1.0;
95	C[2][4] := 1.0;
96
97	(* the sum of Na + Ca is equal to one. *)
98	Cs[3] := 1.0;
99	C[3][1] := 1.0;
100	C[3][2] := 1.0;
101	C[3][3] := 0.0;
102	C[3][4] := 0.0;
103
104	(* cation weights *)
105	w[1] := 30.9895; (* 22.9898 + 15.9994(1/2) )
106	w[2] := 56.0774; (* 40.078 + 15.9994 *)
107	w[3] := 50.9806; (* 26.9815 + 15.9994(3/2) )
108	w[4] := 60.0843; (* 28.0855 + 15.9994(2/1) )
109
110	y[1] := 11.19/100 {};
111	y[2] := 1.07/100 {};
112	y[3] := 20.35/100 {};
113	y[4] := 67.39/100 {};
114
115	k := 2.62925;
116
117	s[1] := 0.05 {};
118	s[2] := 0.05 {};
119	s[3] := 0.05 {};
120	s[4] := 0.05 {};
121
122	END values;
123	METHOD default_self;
124	x[1] := 11.29/100 {};
125	x[2] := 1.01/100 {};
126	x[3] := 20.31/100 {};
127	x[4] := 67.30/100 {};
128	END default_self;
129
130	METHOD on_load;
131	RUN reset;
132	RUN values;
133	RUN specify;
134	END on_load;
135
136	METHOD self_test;
137	END self_test;
138
139	END formula;