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Up to [local] / OpenXM_contrib / PHC / Ada / Continuation

Import the second public release of PHCpack.

OKed by Jan Verschelde.

with Standard_Floating_Numbers;          use Standard_Floating_Numbers;
with Continuation_Data;                  use Continuation_Data;

package Continuation_Parameters is

-- DESCRIPTION :
--   This package contains all important parameters and the default values.

-- GLOBAL MONITOR :

  condition : natural := 0;                                             --  1
            -- low = smooth paths, high = difficult path

  block_size : natural := 1;                                            --  2
            -- number of paths tracked simultaneously:
            -- sequential, parallel or a combination of both.

  max_steps : natural := 500*(condition+1);                             --  3
            -- maximum number of steps along a path

  start_end_game : double_float := 0.1;                                 --  4
            -- distance from target to start the end game

  endext_order : natural := 0;                                          --  5
            -- order of extrapolator in polyhedral end game

  max_reruns : natural := condition + 1;                                --  6
            -- maximum number of re-runs allowed

-- STEP CONTROL (PREDICTOR) :

  predictor_path_type : natural := 0;                                   --  7
  predictor_endg_type : natural := 0;                                   --  8
            -- predictor types:
            --   0 : secant for x, real for t;
            --   1 : secant for x, complex for t;
            --   2 : secant for x, geometric for t;
            --   3 : tangens for x, real for t;
            --   4 : tangens for x, complex for t;
            --   5 : tangens for x, geometric for t;
            --   6 : Hermite for x, real for t;

  min_path_step_size : double_float := 10.0**(-6 - condition/4);        --  9
  min_endg_step_size : double_float := 10.0**(-8 - condition/4);        -- 10
            -- minimum step size along a path and at end of path

  max_path_step_size : double_float := 0.1/(double_float(condition+1)); -- 11
  max_endg_step_size : double_float := 0.1/(double_float(condition+2)); -- 12
            -- maximum step size along a path and at end of path

  reduction_path_factor : double_float := 0.70;                         -- 13
  reduction_endg_factor : double_float := 0.50;                         -- 14
            -- reduction factor for step size along a path and at end

  expansion_path_factor : double_float := 1.25;                         -- 15
  expansion_endg_factor : double_float := 1.10;                         -- 16
            -- expansion factor for step size

  success_path_steps : natural := 1 + 2*condition;                      -- 17
  success_endg_steps : natural := 1 + 4*condition;                      -- 18
            -- threshold on number of successful steps
            -- before expanding step size

  power_of_t : positive := 1;   -- power of t in the (polyhedral) homotopy

-- PATH CLOSENESS (CORRECTOR) :

  max_path_iter : natural := 4;                                         -- 19
  max_endg_iter : natural := 4;                                         -- 20
            -- maximum number of iterations for one corrector step
            -- along the path and at the end of the path

  relative_path_residual : double_float := 10.0**(-9 - condition);      -- 21
  relative_endg_residual : double_float := 10.0**(-11 - condition);     -- 22
  absolute_path_residual : double_float := 10.0**(-9 - condition);      -- 23
  absolute_endg_residual : double_float := 10.0**(-11 - condition);     -- 24
            -- desired precision for residuals along the path and at end
            --  |F(x)| < *_residual, once relative and once absolute

  relative_path_correction : double_float := 10.0**(-9 - condition);    -- 25
  relative_endg_correction : double_float := 10.0**(-11 - condition);   -- 26
  absolute_path_correction : double_float := 10.0**(-9 - condition);    -- 27
  absolute_endg_correction : double_float := 10.0**(-11 - condition);   -- 28
            -- desired precision for corrections along the path and at end
            --  |delta(x)| < *_correction, once relative and once absolute

-- SOLUTIONS (TOLERANCES) :

  tol_path_inverse_condition : double_float := 10.0**(-4);              -- 29
  tol_endg_inverse_condition : double_float := 10.0**(-12);             -- 30
            -- tolerance for inverse condition of jacobian to
            -- decide whether solution is singular or not

  tol_path_distance : double_float := 10.0**(-4);                       -- 31
  tol_endg_distance : double_float := 10.0**(-12);                      -- 32
            -- tolerance for two solutions x1, x2 to be clustered,
            -- when |x1(k) - x2(k)| < tol_*_distance, for all k

  tol_path_at_infinity : double_float := 10.0**4;                       -- 33
  tol_endg_at_infinity : double_float := 10.0**12;                      -- 34
            -- tolerance for a solution x to lie a infinity,
            -- when |x(k)| > tol_at_infinity, for a certain k

-- TUNING OF THE PARAMETERS :

  procedure Tune ( estimate_for_condition : in natural );

  -- DESCRIPTION :
  --   Given an estimate for the condition of the homotopy, parameters
  --   will be set, according to the formulas in the defaults.

  procedure Tune_Endgm_Pred ( extrapolation_order : in natural );

  -- DESCRIPTION :
  --   Determines the settings for the predictor in the end game,
  --   depending on the extrapolation order.

-- CREATING PARAMETER SETS :

  function Create_for_Path return Pred_Pars;
  function Create_End_Game return Pred_Pars;
  function Create_for_Path return Corr_Pars;
  function Create_End_Game return Corr_Pars;

  -- DESCRIPTION :
  --   Given the values for the parameters, sets of predictor and
  --   corrector parameters will be created.

end Continuation_Parameters;