File: [local] / OpenXM_contrib / PHC / Ada / Continuation / standard_root_refiners.ads (download)
Revision 1.1.1.1 (vendor branch), Sun Oct 29 17:45:22 2000 UTC (23 years, 10 months ago) by maekawa
Branch: PHC, MAIN
CVS Tags: v2, maekawa-ipv6, RELEASE_1_2_3, RELEASE_1_2_2_KNOPPIX_b, RELEASE_1_2_2_KNOPPIX, RELEASE_1_2_2, RELEASE_1_2_1, HEAD Changes since 1.1: +0 -0
lines
Import the second public release of PHCpack.
OKed by Jan Verschelde.
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with text_io; use text_io;
with Standard_Floating_Numbers; use Standard_Floating_Numbers;
with Standard_Complex_Poly_Systems; use Standard_Complex_Poly_Systems;
with Standard_Complex_Poly_SysFun; use Standard_Complex_Poly_SysFun;
with Standard_Complex_Jaco_Matrices; use Standard_Complex_Jaco_Matrices;
with Standard_Complex_Solutions; use Standard_Complex_Solutions;
package Standard_Root_Refiners is
-- DESCRIPTION:
-- The aim of this package is to provide some routines to
-- perform root refining, to validate the approximate solutions.
-- It can be used as a postprocessor to check the computed roots,
-- or, as preprocessor, to find some suitable starting values for
-- the continuation procedure.
-- The basic root refiner is Newton's method. There are four versions:
-- + reporting/silent : with/without intermediate output
-- + standard/function evaluator.
-- NEWTON'S METHOD :
procedure Silent_Newton
( p_eval : in Eval_Poly_Sys; j_eval : in Eval_Jaco_Mat;
zero : in out Solution; epsxa,epsfa : in double_float;
numit : in out natural; max : in natural; fail : out boolean );
procedure Silent_Newton
( p_eval : in Standard_Complex_Poly_SysFun.Evaluator;
j_eval : in Standard_Complex_Jaco_Matrices.Evaluator;
zero : in out Solution; epsxa,epsfa : in double_float;
numit : in out natural; max : in natural; fail : out boolean );
procedure Reporting_Newton
( file : in file_type;
p_eval : in Eval_Poly_Sys; j_eval : in Eval_Jaco_Mat;
zero : in out Solution; epsxa,epsfa : in double_float;
numit : in out natural; max : in natural; fail : out boolean );
procedure Reporting_Newton
( file : in file_type;
p_eval : in Standard_Complex_Poly_SysFun.Evaluator;
j_eval : in Standard_Complex_Jaco_Matrices.Evaluator;
zero : in out Solution; epsxa,epsfa : in double_float;
numit : in out natural; max : in natural; fail : out boolean );
-- DESCRIPTION :
-- Newton's method is applied to refine the approximation of a root.
-- The stopping criteria are:
-- * numit > max (maximum number of iterations is exceeded);
-- * zero.err < epsxa (accuracy for x is reached);
-- * zero.res < epsfa (tolerance for residual is reached).
-- When one of these conditions is fulfilled, the procedure stops.
-- ON ENTRY :
-- file to write intermediate results on;
-- p_eval evaluable form of the polynomial system;
-- j_eval evaluable form of the Jacobian matrix;
-- zero starting value;
-- epsxa maximum absolute error on the zero;
-- epsfa maximum absolute value of the residue;
-- numit number of iterations, to be initialized with zero;
-- max maximum number of iterations.
-- ON RETURN :
-- zero refined root;
-- numit number of iterations performed;
-- fail is true when the desired precision is not reached.
-- APPLICATION of Newton's Method on a list of solutions.
-- The silent versions simply perform the calculations.
-- The reporting root refiners allow the output of intermediate results and
-- produce a summary of the calculations.
-- With each version, an additional output parameter can be supplied to
-- contain only those solutions that satisfy the accuracy requirements.
procedure Silent_Root_Refiner
( p : in Poly_Sys; sols : in out Solution_List;
epsxa,epsfa,tolsing : in double_float;
numit : in out natural; max : in natural );
procedure Silent_Root_Refiner
( p : in Standard_Complex_Poly_SysFun.Evaluator;
j : in Standard_Complex_Jaco_Matrices.Evaluator;
sols : in out Solution_List;
epsxa,epsfa,tolsing : in double_float;
numit : in out natural; max : in natural );
procedure Silent_Root_Refiner
( p : in Poly_Sys; sols,refsols : in out Solution_List;
epsxa,epsfa,tolsing : in double_float;
numit : in out natural; max : in natural );
procedure Silent_Root_Refiner
( p : in Standard_Complex_Poly_SysFun.Evaluator;
j : in Standard_Complex_Jaco_Matrices.Evaluator;
sols,refsols : in out Solution_List;
epsxa,epsfa,tolsing : in double_float;
numit : in out natural; max : in natural );
procedure Reporting_Root_Refiner
( file : in file_type;
p : in Poly_Sys; sols : in out Solution_List;
epsxa,epsfa,tolsing : in double_float;
numit : in out natural; max : in natural; wout : in boolean );
procedure Reporting_Root_Refiner
( file : in file_type;
p : in Standard_Complex_Poly_SysFun.Evaluator;
j : in Standard_Complex_Jaco_Matrices.Evaluator;
sols : in out Solution_List;
epsxa,epsfa,tolsing : in double_float;
numit : in out natural; max : in natural; wout : in boolean );
procedure Reporting_Root_Refiner
( file : in file_type;
p : in Poly_Sys; sols,refsols : in out Solution_List;
epsxa,epsfa,tolsing : in double_float;
numit : in out natural; max : in natural; wout : in boolean );
procedure Reporting_Root_Refiner
( file : in file_type;
p : in Standard_Complex_Poly_SysFun.Evaluator;
j : in Standard_Complex_Jaco_Matrices.Evaluator;
sols,refsols : in out Solution_List;
epsxa,epsfa,tolsing : in double_float;
numit : in out natural; max : in natural; wout : in boolean );
-- DESCRIPTION :
-- The list of solutions sols is refined w.r.t. the system p.
-- The multiplicity of each solution in sols is determined as follows:
-- m = 0 : if the solution is singular and probably non isolated
-- or if the solution lies at infinity ( in fact no solution );
-- m = 1 : if the solution is regular;
-- m > 1 : a multiple solution with multiplicity m.
-- ON ENTRY :
-- file file for writing diagnostics on;
-- p a polynomial system;
-- j Jacobian matrix of p;
-- sols the start solutions;
-- epsxa maximum absolute error on the zero;
-- epsfa maximum absolute value for the residue;
-- tolsing tolerance on inverse condition number for singular solution;
-- numit the number of iterations, to be initialized with zero;
-- max maximum number of iterations per zero;
-- wout has to be true when intermediate output is wanted.
-- ON RETURN :
-- sols a list of computed solutions;
-- refsols only those solutions which satisfy the given accuracy;
-- numit the number of iterations.
end Standard_Root_Refiners;