Annotation of OpenXM_contrib/PHC/Ada/Continuation/standard_root_refiners.ads, Revision 1.1.1.1
1.1 maekawa 1: with text_io; use text_io;
2: with Standard_Floating_Numbers; use Standard_Floating_Numbers;
3: with Standard_Complex_Poly_Systems; use Standard_Complex_Poly_Systems;
4: with Standard_Complex_Poly_SysFun; use Standard_Complex_Poly_SysFun;
5: with Standard_Complex_Jaco_Matrices; use Standard_Complex_Jaco_Matrices;
6: with Standard_Complex_Solutions; use Standard_Complex_Solutions;
7:
8: package Standard_Root_Refiners is
9:
10: -- DESCRIPTION:
11: -- The aim of this package is to provide some routines to
12: -- perform root refining, to validate the approximate solutions.
13: -- It can be used as a postprocessor to check the computed roots,
14: -- or, as preprocessor, to find some suitable starting values for
15: -- the continuation procedure.
16:
17: -- The basic root refiner is Newton's method. There are four versions:
18: -- + reporting/silent : with/without intermediate output
19: -- + standard/function evaluator.
20:
21: -- NEWTON'S METHOD :
22:
23: procedure Silent_Newton
24: ( p_eval : in Eval_Poly_Sys; j_eval : in Eval_Jaco_Mat;
25: zero : in out Solution; epsxa,epsfa : in double_float;
26: numit : in out natural; max : in natural; fail : out boolean );
27:
28: procedure Silent_Newton
29: ( p_eval : in Standard_Complex_Poly_SysFun.Evaluator;
30: j_eval : in Standard_Complex_Jaco_Matrices.Evaluator;
31: zero : in out Solution; epsxa,epsfa : in double_float;
32: numit : in out natural; max : in natural; fail : out boolean );
33:
34: procedure Reporting_Newton
35: ( file : in file_type;
36: p_eval : in Eval_Poly_Sys; j_eval : in Eval_Jaco_Mat;
37: zero : in out Solution; epsxa,epsfa : in double_float;
38: numit : in out natural; max : in natural; fail : out boolean );
39:
40: procedure Reporting_Newton
41: ( file : in file_type;
42: p_eval : in Standard_Complex_Poly_SysFun.Evaluator;
43: j_eval : in Standard_Complex_Jaco_Matrices.Evaluator;
44: zero : in out Solution; epsxa,epsfa : in double_float;
45: numit : in out natural; max : in natural; fail : out boolean );
46:
47: -- DESCRIPTION :
48: -- Newton's method is applied to refine the approximation of a root.
49: -- The stopping criteria are:
50: -- * numit > max (maximum number of iterations is exceeded);
51: -- * zero.err < epsxa (accuracy for x is reached);
52: -- * zero.res < epsfa (tolerance for residual is reached).
53: -- When one of these conditions is fulfilled, the procedure stops.
54:
55: -- ON ENTRY :
56: -- file to write intermediate results on;
57: -- p_eval evaluable form of the polynomial system;
58: -- j_eval evaluable form of the Jacobian matrix;
59: -- zero starting value;
60: -- epsxa maximum absolute error on the zero;
61: -- epsfa maximum absolute value of the residue;
62: -- numit number of iterations, to be initialized with zero;
63: -- max maximum number of iterations.
64:
65: -- ON RETURN :
66: -- zero refined root;
67: -- numit number of iterations performed;
68: -- fail is true when the desired precision is not reached.
69:
70: -- APPLICATION of Newton's Method on a list of solutions.
71: -- The silent versions simply perform the calculations.
72: -- The reporting root refiners allow the output of intermediate results and
73: -- produce a summary of the calculations.
74: -- With each version, an additional output parameter can be supplied to
75: -- contain only those solutions that satisfy the accuracy requirements.
76:
77: procedure Silent_Root_Refiner
78: ( p : in Poly_Sys; sols : in out Solution_List;
79: epsxa,epsfa,tolsing : in double_float;
80: numit : in out natural; max : in natural );
81:
82: procedure Silent_Root_Refiner
83: ( p : in Standard_Complex_Poly_SysFun.Evaluator;
84: j : in Standard_Complex_Jaco_Matrices.Evaluator;
85: sols : in out Solution_List;
86: epsxa,epsfa,tolsing : in double_float;
87: numit : in out natural; max : in natural );
88:
89: procedure Silent_Root_Refiner
90: ( p : in Poly_Sys; sols,refsols : in out Solution_List;
91: epsxa,epsfa,tolsing : in double_float;
92: numit : in out natural; max : in natural );
93:
94: procedure Silent_Root_Refiner
95: ( p : in Standard_Complex_Poly_SysFun.Evaluator;
96: j : in Standard_Complex_Jaco_Matrices.Evaluator;
97: sols,refsols : in out Solution_List;
98: epsxa,epsfa,tolsing : in double_float;
99: numit : in out natural; max : in natural );
100:
101: procedure Reporting_Root_Refiner
102: ( file : in file_type;
103: p : in Poly_Sys; sols : in out Solution_List;
104: epsxa,epsfa,tolsing : in double_float;
105: numit : in out natural; max : in natural; wout : in boolean );
106:
107: procedure Reporting_Root_Refiner
108: ( file : in file_type;
109: p : in Standard_Complex_Poly_SysFun.Evaluator;
110: j : in Standard_Complex_Jaco_Matrices.Evaluator;
111: sols : in out Solution_List;
112: epsxa,epsfa,tolsing : in double_float;
113: numit : in out natural; max : in natural; wout : in boolean );
114:
115: procedure Reporting_Root_Refiner
116: ( file : in file_type;
117: p : in Poly_Sys; sols,refsols : in out Solution_List;
118: epsxa,epsfa,tolsing : in double_float;
119: numit : in out natural; max : in natural; wout : in boolean );
120:
121: procedure Reporting_Root_Refiner
122: ( file : in file_type;
123: p : in Standard_Complex_Poly_SysFun.Evaluator;
124: j : in Standard_Complex_Jaco_Matrices.Evaluator;
125: sols,refsols : in out Solution_List;
126: epsxa,epsfa,tolsing : in double_float;
127: numit : in out natural; max : in natural; wout : in boolean );
128:
129: -- DESCRIPTION :
130: -- The list of solutions sols is refined w.r.t. the system p.
131: -- The multiplicity of each solution in sols is determined as follows:
132: -- m = 0 : if the solution is singular and probably non isolated
133: -- or if the solution lies at infinity ( in fact no solution );
134: -- m = 1 : if the solution is regular;
135: -- m > 1 : a multiple solution with multiplicity m.
136:
137: -- ON ENTRY :
138: -- file file for writing diagnostics on;
139: -- p a polynomial system;
140: -- j Jacobian matrix of p;
141: -- sols the start solutions;
142: -- epsxa maximum absolute error on the zero;
143: -- epsfa maximum absolute value for the residue;
144: -- tolsing tolerance on inverse condition number for singular solution;
145: -- numit the number of iterations, to be initialized with zero;
146: -- max maximum number of iterations per zero;
147: -- wout has to be true when intermediate output is wanted.
148:
149: -- ON RETURN :
150: -- sols a list of computed solutions;
151: -- refsols only those solutions which satisfy the given accuracy;
152: -- numit the number of iterations.
153:
154: end Standard_Root_Refiners;
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