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Annotation of OpenXM_contrib/PHC/Ada/Continuation/multprec_root_refiners.ads, Revision 1.1.1.1

1.1       maekawa     1: with text_io;                            use text_io;
                      2: with Multprec_Floating_Numbers;          use Multprec_Floating_Numbers;
                      3: with Multprec_Complex_Poly_Systems;      use Multprec_Complex_Poly_Systems;
                      4: with Multprec_Complex_Poly_SysFun;       use Multprec_Complex_Poly_SysFun;
                      5: with Multprec_Complex_Jaco_Matrices;     use Multprec_Complex_Jaco_Matrices;
                      6: with Multprec_Complex_Solutions;         use Multprec_Complex_Solutions;
                      7:
                      8: package Multprec_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 two versions
                     18: --   provided : a silent and a reporting version.  The reporting version puts
                     19: --   intermediate results on file during the iterations, while the silent
                     20: --   version simply returns the refined solutions.
                     21:
                     22: -- NEWTON'S METHOD :
                     23:
                     24:   procedure Silent_Newton
                     25:                ( p_eval : in Eval_Poly_Sys; j_eval : in Eval_Jaco_Mat;
                     26:                  zero : in out Solution; epsxa,epsfa : in Floating_Number;
                     27:                  numit : in out natural; max : in natural; fail : out boolean );
                     28:
                     29:   procedure Reporting_Newton
                     30:                ( file : in file_type;
                     31:                  p_eval : in Eval_Poly_Sys; j_eval : in Eval_Jaco_Mat;
                     32:                  zero : in out Solution; epsxa,epsfa : in Floating_Number;
                     33:                  numit : in out natural; max : in natural; fail : out boolean );
                     34:
                     35:   -- DESCRIPTION :
                     36:   --   Newton's method is applied to refine the approximation of a root.
                     37:   --   The stopping criteria are:
                     38:   --     * numit > max   (maximum number of iterations is exceeded);
                     39:   --     * zero.err < epsxa (accuracy for x is reached);
                     40:   --     * zero.res < epsfa (tolerance for residual is reached).
                     41:   --   When one of these conditions is fulfilled, the procedure stops.
                     42:
                     43:   -- ON ENTRY :
                     44:   --   file      to write intermediate results on;
                     45:   --   p_eval    evaluable form of the polynomial system;
                     46:   --   j_eval    evaluable form of the Jacobian matrix;
                     47:   --   zero      starting value;
                     48:   --   epsxa     maximum absolute error on the zero;
                     49:   --   epsfa     maximum absolute value of the residue;
                     50:   --   numit     number of iterations, to be initialized with zero;
                     51:   --   max       maximum number of iterations.
                     52:
                     53:   -- ON RETURN :
                     54:   --   zero      refined root;
                     55:   --   numit     number of iterations performed;
                     56:   --   fail      is true when the desired precision is not reached.
                     57:
                     58: -- APPLICATION of Newton's Method on a list of solutions.
                     59: --   The silent versions simply perform the calculations.
                     60: --   The reporting root refiners allow the output of intermediate results and
                     61: --   produce a summary of the calculations.
                     62: --   With each version, an additional output parameter can be supplied to
                     63: --   contain only those solutions that satisfy the accuracy requirements.
                     64:
                     65:   procedure Silent_Root_Refiner
                     66:                ( p : in Poly_Sys; sols : in out Solution_List;
                     67:                  epsxa,epsfa,tolsing : in Floating_Number;
                     68:                  numit : in out natural; max : in natural );
                     69:
                     70:   procedure Silent_Root_Refiner
                     71:                ( p : in Poly_Sys; sols,refsols : in out Solution_List;
                     72:                  epsxa,epsfa,tolsing : in Floating_Number;
                     73:                  numit : in out natural; max : in natural );
                     74:
                     75:   procedure Reporting_Root_Refiner
                     76:                ( file : in file_type;
                     77:                  p : in Poly_Sys; sols : in out Solution_List;
                     78:                  epsxa,epsfa,tolsing : in Floating_Number;
                     79:                  numit : in out natural; max : in natural; wout : in boolean );
                     80:
                     81:   procedure Reporting_Root_Refiner
                     82:                ( file : in file_type;
                     83:                  p : in Poly_Sys; sols,refsols : in out Solution_List;
                     84:                  epsxa,epsfa,tolsing : in Floating_Number;
                     85:                  numit : in out natural; max : in natural; wout : in boolean );
                     86:
                     87:   -- DESCRIPTION :
                     88:   --   The list of solutions sols is refined w.r.t. the system p.
                     89:   --   The multiplicity of each solution in sols is determined as follows:
                     90:   --     m = 0 : if the solution is singular and probably non isolated
                     91:   --             or if the solution lies at infinity ( in fact no solution );
                     92:   --     m = 1 : if the solution is regular;
                     93:   --     m > 1 : a multiple solution with multiplicity m.
                     94:
                     95:   -- ON ENTRY :
                     96:   --   file      file for writing diagnostics on;
                     97:   --   p         a polynomial system;
                     98:   --   sols      the start solutions;
                     99:   --   epsxa     maximum absolute error on the zero;
                    100:   --   epsfa     maximum absolute value for the residue;
                    101:   --   tolsing   tolerance on inverse condition number for singular solution;
                    102:   --   numit     the number of iterations, to be initialized with zero;
                    103:   --   max       maximum number of iterations per zero;
                    104:   --   wout      has to be true when intermediate output is wanted.
                    105:
                    106:   -- ON RETURN :
                    107:   --   sols      a list of computed solutions;
                    108:   --   refsols   only those solutions which satisfy the given accuracy;
                    109:   --   numit     the number of iterations.
                    110:
                    111: end Multprec_Root_Refiners;